155:@0.890754:0.963104:0.932133:0.963104:0.932133:0.941283:0.890754:0.941283:0.000000:0.000000:0.000000
Matemática:@0.795130:0.956142:0.879896:0.956142:0.879896:0.943479:0.795130:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.º BG:@0.837761:0.967458:0.879897:0.967458:0.879897:0.954794:0.837761:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.096359:0.548158:0.110585:0.548158:0.110585:0.531257:0.096359:0.531257:0.000000:0.000000
  Resolvamos el siguiente problema: Si fabricar una silla toma 3 horas y una mesa, 4 horas; :@0.110585:0.548158:0.773754:0.548158:0.773754:0.531769:0.110585:0.531769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y tenemos 16 horas disponibles, ¿qué combinaciones enteras son posibles?:@0.124848:0.564754:0.676914:0.564754:0.676914:0.548366:0.124848:0.548366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 1. :@0.102121:0.159095:0.157756:0.159095:0.157756:0.143517:0.102121:0.143517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la ecuación dada despejamos  .:@0.157756:0.159095:0.391366:0.159095:0.391366:0.144196:0.157756:0.144196:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.381650:0.159095:0.388452:0.159095:0.388452:0.144221:0.381650:0.144221:0.000000
2:@0.403670:0.182290:0.412663:0.182290:0.412663:0.165901:0.403670:0.165901:0.000000
3:@0.438590:0.182290:0.447583:0.182290:0.447583:0.165901:0.438590:0.165901:0.000000
30;     :@0.475704:0.182290:0.519911:0.182290:0.519911:0.165901:0.475704:0.165901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.556748:0.173355:0.565741:0.173355:0.565741:0.156966:0.556748:0.156966:0.000000
3:@0.551404:0.193285:0.560397:0.193285:0.560397:0.176896:0.551404:0.176896:0.000000
10:@0.593843:0.182290:0.611736:0.182290:0.611736:0.165901:0.593843:0.165901:0.000000:0.000000
x:@0.413455:0.182290:0.420918:0.182290:0.420918:0.165929:0.413455:0.165929:0.000000
y:@0.448633:0.182290:0.456115:0.182290:0.456115:0.165929:0.448633:0.165929:0.000000
y:@0.518161:0.182290:0.525642:0.182290:0.525642:0.165929:0.518161:0.165929:0.000000
x:@0.569887:0.182290:0.577350:0.182290:0.577350:0.165929:0.569887:0.165929:0.000000
+:@0.425451:0.181875:0.399542:0.181875:0.399542:0.164933:0.425451:0.164933:0.000000
=:@0.461477:0.181875:0.435568:0.181875:0.435568:0.164933:0.461477:0.164933:0.000000
=:@0.530986:0.181875:0.541103:0.181875:0.541103:0.164933:0.530986:0.164933:0.000000
−:@0.546687:0.172940:0.556804:0.172940:0.556804:0.155998:0.546687:0.155998:0.000000
+:@0.581865:0.181875:0.591982:0.181875:0.591982:0.164933:0.581865:0.164933:0.000000
Paso 2. :@0.102121:0.212408:0.157756:0.212408:0.157756:0.196830:0.102121:0.196830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por las condiciones iniciales  ,   deben ser número enteros, entonces asignamos valores múltiplos de 3:@0.157756:0.212408:0.840177:0.212408:0.840177:0.197509:0.157756:0.197509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y x:@0.345366:0.212408:0.365536:0.212408:0.365536:0.197535:0.345366:0.197535:0.000000:0.000000:0.000000
a la variable   y obtenemos los valores de  , completamos la tabla.:@0.102121:0.227496:0.541064:0.227496:0.541064:0.212597:0.102121:0.212597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.184158:0.227496:0.190942:0.227496:0.190942:0.212622:0.184158:0.212622:0.000000
y:@0.380392:0.227496:0.387193:0.227496:0.387193:0.212622:0.380392:0.212622:0.000000
Paso 3. :@0.102121:0.301513:0.157756:0.301513:0.157756:0.285935:0.102121:0.285935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las posibles soluciones son los pares :@0.157756:0.301513:0.405887:0.301513:0.405887:0.286614:0.157756:0.286614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ordenados: (–9, 16); (–6, 14); (–3, 12); (0, 10); (3, 8); (6, 6); :@0.102121:0.316601:0.468680:0.316601:0.468680:0.301702:0.102121:0.301702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(9, 4); (12, 2), (15, 0), entre otras.:@0.102121:0.331689:0.308105:0.331689:0.308105:0.316790:0.102121:0.316790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De todas estas soluciones, nos interesan las positivas; :@0.102121:0.350334:0.458341:0.350334:0.458341:0.335435:0.102121:0.335435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en este caso: (0, 10); (3, 8); (6, 6); (9, 4); (12, 2), (15, 0), :@0.102121:0.365422:0.445862:0.365422:0.445862:0.350523:0.102121:0.350523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre otras.:@0.102121:0.380510:0.176567:0.380510:0.176567:0.365611:0.102121:0.365611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Nota: en un contexto real, por ejemplo en producción, :@0.102121:0.399155:0.467788:0.399155:0.467788:0.384256:0.102121:0.384256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
solo se consideran soluciones positivas en el primer :@0.102121:0.414243:0.449576:0.414243:0.449576:0.399344:0.102121:0.399344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuadrante, donde :@0.102121:0.429331:0.224263:0.429331:0.224263:0.414432:0.102121:0.414432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.225289:0.429253:0.232006:0.429253:0.232006:0.414527:0.225289:0.414527:0.000000
y:@0.266088:0.429253:0.272821:0.429253:0.272821:0.414527:0.266088:0.414527:0.000000
≥:@0.236550:0.428879:0.204856:0.428879:0.204856:0.413631:0.236550:0.413631:0.000000
≥:@0.277349:0.428879:0.245655:0.428879:0.245655:0.413631:0.277349:0.413631:0.000000
0, :@0.248839:0.429253:0.266088:0.429253:0.266088:0.414503:0.248839:0.414503:0.000000:0.000000:0.000000
0.:@0.289638:0.429253:0.300534:0.429253:0.300534:0.414503:0.289638:0.414503:0.000000:0.000000
Paso 1. :@0.102121:0.589028:0.157756:0.589028:0.157756:0.573450:0.102121:0.573450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Designamos las variables que intervienen en el problema.:@0.157756:0.589028:0.541982:0.589028:0.541982:0.574129:0.157756:0.574129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Número de sillas: :@0.102121:0.607674:0.219087:0.607674:0.219087:0.592775:0.102121:0.592775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.219087:0.607674:0.225871:0.607674:0.225871:0.592800:0.219087:0.592800:0.000000
Número mesas:  :@0.102121:0.622761:0.213089:0.622761:0.213089:0.607862:0.102121:0.607862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.213089:0.622761:0.219891:0.622761:0.219891:0.607887:0.213089:0.607887:0.000000
Ecuación que modela el problema: 3  + 4  = 16; Despejamos  : :@0.102121:0.649177:0.525248:0.649177:0.525248:0.634278:0.102121:0.634278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.346100:0.649177:0.352885:0.649177:0.352885:0.634303:0.346100:0.634303:0.000000
y:@0.378382:0.649177:0.385183:0.649177:0.385183:0.634303:0.378382:0.634303:0.000000
y:@0.511863:0.649177:0.518665:0.649177:0.518665:0.634303:0.511863:0.634303:0.000000
y:@0.529015:0.649182:0.535748:0.649182:0.535748:0.634457:0.529015:0.634457:0.000000
x:@0.572550:0.641154:0.579267:0.641154:0.579267:0.626429:0.572550:0.626429:0.000000
=:@0.540558:0.648809:0.549663:0.648809:0.549663:0.633561:0.540558:0.633561:0.000000
−:@0.554693:0.640782:0.563798:0.640782:0.563798:0.625534:0.554693:0.625534:0.000000
+:@0.584659:0.648809:0.593765:0.648809:0.593765:0.633561:0.584659:0.633561:0.000000
3:@0.563746:0.641154:0.571839:0.641154:0.571839:0.626404:0.563746:0.626404:0.000000
4:@0.563503:0.659083:0.571596:0.659083:0.571596:0.644333:0.563503:0.644333:0.000000
4:@0.597003:0.649182:0.605096:0.649182:0.605096:0.634432:0.597003:0.634432:0.000000
Paso 2. :@0.102121:0.678128:0.157756:0.678128:0.157756:0.662550:0.102121:0.662550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por las condiciones iniciales  ,   deben ser número enteros, entonces asignamos valores múltiplos de 4:@0.157756:0.678128:0.840177:0.678128:0.840177:0.663229:0.157756:0.663229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y x:@0.345366:0.678128:0.365536:0.678128:0.365536:0.663254:0.345366:0.663254:0.000000:0.000000:0.000000
a la variable   y obtenemos los valores de  , completamos la tabla.:@0.102121:0.693215:0.541064:0.693215:0.541064:0.678316:0.102121:0.678316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.184158:0.693215:0.190942:0.693215:0.190942:0.678342:0.184158:0.678342:0.000000
y:@0.380392:0.693215:0.387193:0.693215:0.387193:0.678342:0.380392:0.678342:0.000000
Paso 3. :@0.102121:0.888399:0.157756:0.888399:0.157756:0.872821:0.102121:0.872821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De todas las soluciones nos interesan las positivas: (0, 4) y (4, 1). :@0.157756:0.888399:0.580163:0.888399:0.580163:0.873500:0.157756:0.873500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Con el tiempo asignado se pueden fabricar 0 sillas y 4 mesas o, 4 sillas y una mesa.:@0.102121:0.907045:0.648057:0.907045:0.648057:0.892146:0.102121:0.892146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.096359:0.118227:0.110585:0.118227:0.110585:0.101326:0.096359:0.101326:0.000000:0.000000
  Consideremos la ecuación lineal 2  + 3  = 30. Obtengamos algunas soluciones y :@0.110585:0.118227:0.717610:0.118227:0.717610:0.101838:0.110585:0.101838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.373863:0.118227:0.381326:0.118227:0.381326:0.101865:0.373863:0.101865:0.000000
y:@0.409373:0.118227:0.416854:0.118227:0.416854:0.101865:0.409373:0.101865:0.000000
de ellas seleccionemos, las positivas.:@0.124848:0.134823:0.390238:0.134823:0.390238:0.118434:0.124848:0.118434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.163449:0.253386:0.171356:0.253386:0.171356:0.238022:0.163449:0.238022:0.000000
–9:@0.216118:0.253386:0.232670:0.253386:0.232670:0.238487:0.216118:0.238487:0.000000:0.000000
–6:@0.292091:0.253386:0.308642:0.253386:0.308642:0.238487:0.292091:0.238487:0.000000:0.000000
–3:@0.368063:0.253386:0.384614:0.253386:0.384614:0.238487:0.368063:0.238487:0.000000:0.000000
0:@0.448223:0.253386:0.456398:0.253386:0.456398:0.238487:0.448223:0.238487:0.000000
3:@0.524195:0.253386:0.532370:0.253386:0.532370:0.238487:0.524195:0.238487:0.000000
6:@0.600167:0.253386:0.608342:0.253386:0.608342:0.238487:0.600167:0.238487:0.000000
9:@0.676139:0.253386:0.684314:0.253386:0.684314:0.238487:0.676139:0.238487:0.000000
12:@0.748024:0.253386:0.764374:0.253386:0.764374:0.238487:0.748024:0.238487:0.000000:0.000000
15:@0.823996:0.253386:0.840346:0.253386:0.840346:0.238487:0.823996:0.238487:0.000000:0.000000
y:@0.163399:0.274773:0.171306:0.274773:0.171306:0.259409:0.163399:0.259409:0.000000
16:@0.216169:0.274773:0.232519:0.274773:0.232519:0.259874:0.216169:0.259874:0.000000:0.000000
14:@0.292141:0.274773:0.308491:0.274773:0.308491:0.259874:0.292141:0.259874:0.000000:0.000000
12:@0.368113:0.274773:0.384463:0.274773:0.384463:0.259874:0.368113:0.259874:0.000000:0.000000
10:@0.444085:0.274773:0.460435:0.274773:0.460435:0.259874:0.444085:0.259874:0.000000:0.000000
8:@0.524145:0.274773:0.532320:0.274773:0.532320:0.259874:0.524145:0.259874:0.000000
6:@0.600117:0.274773:0.608292:0.274773:0.608292:0.259874:0.600117:0.259874:0.000000
4:@0.676089:0.274773:0.684264:0.274773:0.684264:0.259874:0.676089:0.259874:0.000000
2:@0.752061:0.274773:0.760236:0.274773:0.760236:0.259874:0.752061:0.259874:0.000000
0:@0.828033:0.274773:0.836208:0.274773:0.836208:0.259874:0.828033:0.259874:0.000000
–10:@0.645688:0.490019:0.666140:0.490019:0.666140:0.477929:0.645688:0.477929:0.000000:0.000000:0.000000
–5:@0.652564:0.471884:0.666140:0.471884:0.666140:0.459794:0.652564:0.459794:0.000000:0.000000
8:@0.658353:0.384024:0.665228:0.384024:0.665228:0.371934:0.658353:0.371934:0.000000
2:@0.658353:0.437424:0.665228:0.437424:0.665228:0.425334:0.658353:0.425334:0.000000
4:@0.658353:0.419067:0.665228:0.419067:0.665228:0.406977:0.658353:0.406977:0.000000
6:@0.658353:0.401264:0.665228:0.401264:0.665228:0.389174:0.658353:0.389174:0.000000
10:@0.651478:0.365878:0.665228:0.365878:0.665228:0.353788:0.651478:0.353788:0.000000:0.000000
12:@0.651478:0.348145:0.665228:0.348145:0.665228:0.336055:0.651478:0.336055:0.000000:0.000000
14:@0.651478:0.330010:0.665228:0.330010:0.665228:0.317920:0.651478:0.317920:0.000000:0.000000
16:@0.651478:0.312046:0.665228:0.312046:0.665228:0.299956:0.651478:0.299956:0.000000:0.000000
–2 0:@0.639269:0.461705:0.665483:0.461705:0.665483:0.449615:0.639269:0.449615:0.000000:0.000000:0.000000:0.000000
–4:@0.615548:0.461705:0.629124:0.461705:0.629124:0.449615:0.615548:0.449615:0.000000:0.000000
–6:@0.591893:0.461705:0.605469:0.461705:0.605469:0.449615:0.591893:0.449615:0.000000:0.000000
–8:@0.568105:0.461705:0.581681:0.461705:0.581681:0.449615:0.568105:0.449615:0.000000:0.000000
–10:@0.540751:0.461705:0.561203:0.461705:0.561203:0.449615:0.540751:0.449615:0.000000:0.000000:0.000000
–12:@0.513974:0.461705:0.534426:0.461705:0.534426:0.449615:0.513974:0.449615:0.000000:0.000000:0.000000
2:@0.690303:0.461705:0.697179:0.461705:0.697179:0.449615:0.690303:0.449615:0.000000
4:@0.711036:0.461705:0.717911:0.461705:0.717911:0.449615:0.711036:0.449615:0.000000
6:@0.734945:0.461705:0.741820:0.461705:0.741820:0.449615:0.734945:0.449615:0.000000
8:@0.757796:0.461705:0.764671:0.461705:0.764671:0.449615:0.757796:0.449615:0.000000
10 12 14 16 18:@0.781316:0.461705:0.890180:0.461705:0.890180:0.449615:0.781316:0.449615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.658055:0.295521:0.663227:0.295521:0.663227:0.284933:0.658055:0.284933:0.000000
x:@0.899601:0.460903:0.904773:0.460903:0.904773:0.450315:0.899601:0.450315:0.000000
(–9, 16):@0.523642:0.320990:0.564196:0.320990:0.564196:0.308900:0.523642:0.308900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(–6, 14):@0.557428:0.338623:0.597983:0.338623:0.597983:0.326532:0.557428:0.326532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(–3, 12):@0.590317:0.355138:0.630871:0.355138:0.630871:0.343048:0.590317:0.343048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0, 10):@0.674561:0.359584:0.708414:0.359584:0.708414:0.347494:0.674561:0.347494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(3, 8):@0.707463:0.374189:0.734441:0.374189:0.734441:0.362099:0.707463:0.362099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(6, 6):@0.740365:0.393994:0.767343:0.393994:0.767343:0.381904:0.740365:0.381904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(9, 4):@0.774272:0.411093:0.801250:0.411093:0.801250:0.399003:0.774272:0.399003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10:@0.651478:0.365878:0.665228:0.365878:0.665228:0.353788:0.651478:0.353788:0.000000:0.000000
16:@0.853204:0.461705:0.866954:0.461705:0.866954:0.449615:0.853204:0.449615:0.000000:0.000000
16:@0.853204:0.461705:0.866954:0.461705:0.866954:0.449615:0.853204:0.449615:0.000000:0.000000
16:@0.853204:0.461705:0.866954:0.461705:0.866954:0.449615:0.853204:0.449615:0.000000:0.000000
(12, 2):@0.807592:0.429523:0.841445:0.429523:0.841445:0.417433:0.807592:0.417433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(15, 0):@0.844836:0.447045:0.878689:0.447045:0.878689:0.434954:0.844836:0.434954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–1:@0.631719:0.850076:0.645295:0.850076:0.645295:0.837986:0.631719:0.837986:0.000000:0.000000
4:@0.637508:0.760909:0.644383:0.760909:0.644383:0.748818:0.637508:0.748818:0.000000
1:@0.638420:0.814309:0.645295:0.814309:0.645295:0.802218:0.638420:0.802218:0.000000
2:@0.637508:0.795952:0.644383:0.795952:0.644383:0.783862:0.637508:0.783862:0.000000
3:@0.637508:0.778149:0.644383:0.778149:0.644383:0.766058:0.637508:0.766058:0.000000
5:@0.637508:0.742763:0.644383:0.742763:0.644383:0.730673:0.637508:0.730673:0.000000
6:@0.637508:0.725030:0.644383:0.725030:0.644383:0.712940:0.637508:0.712940:0.000000
–1 0:@0.618424:0.838590:0.644638:0.838590:0.644638:0.826499:0.618424:0.826499:0.000000:0.000000:0.000000:0.000000
–2:@0.594703:0.838590:0.608279:0.838590:0.608279:0.826499:0.594703:0.826499:0.000000:0.000000
–3:@0.571048:0.838590:0.584624:0.838590:0.584624:0.826499:0.571048:0.826499:0.000000:0.000000
1:@0.669458:0.838590:0.676334:0.838590:0.676334:0.826499:0.669458:0.826499:0.000000
2:@0.693528:0.838590:0.700403:0.838590:0.700403:0.826499:0.693528:0.826499:0.000000
3:@0.717437:0.838590:0.724313:0.838590:0.724313:0.826499:0.717437:0.826499:0.000000
4:@0.740462:0.838590:0.747337:0.838590:0.747337:0.826499:0.740462:0.826499:0.000000
5:@0.764331:0.838590:0.771206:0.838590:0.771206:0.826499:0.764331:0.826499:0.000000
6:@0.787972:0.838590:0.794847:0.838590:0.794847:0.826499:0.787972:0.826499:0.000000
7:@0.812524:0.838590:0.819399:0.838590:0.819399:0.826499:0.812524:0.826499:0.000000
8:@0.835508:0.838590:0.842383:0.838590:0.842383:0.826499:0.835508:0.826499:0.000000
9:@0.859618:0.838590:0.866493:0.838590:0.866493:0.826499:0.859618:0.826499:0.000000
10:@0.880539:0.838590:0.894289:0.838590:0.894289:0.826499:0.880539:0.826499:0.000000:0.000000
y:@0.637212:0.708054:0.642383:0.708054:0.642383:0.697466:0.637212:0.697466:0.000000
x:@0.901472:0.837800:0.906644:0.837800:0.906644:0.827212:0.901472:0.827212:0.000000
(4, 1):@0.747039:0.808411:0.774017:0.808411:0.774017:0.796320:0.747039:0.796320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0, 4):@0.654190:0.754508:0.681168:0.754508:0.681168:0.742417:0.654190:0.742417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.637508:0.760909:0.644383:0.760909:0.644383:0.748818:0.637508:0.748818:0.000000
6 6 6:@0.787972:0.838590:0.794847:0.838590:0.794847:0.826499:0.787972:0.826499:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.125396:0.718322:0.133303:0.718322:0.133303:0.702958:0.125396:0.702958:0.000000
y:@0.239362:0.718322:0.247270:0.718322:0.247270:0.702958:0.239362:0.702958:0.000000
¿Es entero?:@0.345120:0.718322:0.426418:0.718322:0.426418:0.702958:0.345120:0.702958:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.449287:0.718322:0.512209:0.718322:0.512209:0.702958:0.449287:0.702958:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.125262:0.745945:0.133437:0.745945:0.133437:0.731046:0.125262:0.731046:0.000000
y:@0.186778:0.745939:0.193512:0.745939:0.193512:0.731214:0.186778:0.731214:0.000000
=:@0.198321:0.745566:0.207427:0.745566:0.207427:0.730318:0.198321:0.730318:0.000000
−:@0.212456:0.736619:0.221562:0.736619:0.221562:0.721371:0.212456:0.721371:0.000000
():@0.230738:0.738193:0.251768:0.738193:0.251768:0.718707:0.230738:0.718707:0.000000:0.000000
+=:@0.255756:0.745566:0.288992:0.745566:0.288992:0.730318:0.255756:0.730318:0.000000:0.000000
30:@0.221509:0.736989:0.245192:0.736989:0.245192:0.722239:0.221509:0.722239:0.000000:0.000000
4:@0.227910:0.755835:0.236004:0.755835:0.236004:0.741085:0.227910:0.741085:0.000000
44:@0.268095:0.745939:0.300784:0.745939:0.300784:0.731189:0.268095:0.731189:0.000000:0.000000
(0, 4):@0.464848:0.745949:0.496661:0.745949:0.496661:0.731050:0.464848:0.731050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.125260:0.779997:0.133435:0.779997:0.133435:0.765098:0.125260:0.765098:0.000000
y:@0.188286:0.779699:0.195020:0.779699:0.195020:0.764974:0.188286:0.764974:0.000000
=:@0.199829:0.779325:0.208934:0.779325:0.208934:0.764078:0.199829:0.764078:0.000000
−:@0.213964:0.770380:0.223069:0.770380:0.223069:0.755132:0.213964:0.755132:0.000000
():@0.232246:0.771955:0.253790:0.771955:0.253790:0.752468:0.232246:0.752468:0.000000:0.000000
+=:@0.257783:0.779325:0.291019:0.779325:0.291019:0.764078:0.257783:0.764078:0.000000:0.000000
34:@0.223005:0.770749:0.247219:0.770749:0.247219:0.755999:0.223005:0.755999:0.000000:0.000000
4:@0.229689:0.789594:0.237782:0.789594:0.237782:0.774844:0.229689:0.774844:0.000000
41:@0.270123:0.779699:0.301252:0.779699:0.301252:0.764949:0.270123:0.764949:0.000000:0.000000
(4, 1):@0.464848:0.779991:0.496661:0.779991:0.496661:0.765092:0.464848:0.765092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.125260:0.814378:0.133435:0.814378:0.133435:0.799479:0.125260:0.799479:0.000000
y:@0.182255:0.814331:0.188989:0.814331:0.188989:0.799606:0.182255:0.799606:0.000000
=:@0.193798:0.813958:0.202903:0.813958:0.202903:0.798710:0.193798:0.798710:0.000000
−:@0.207933:0.805011:0.217038:0.805011:0.217038:0.789763:0.207933:0.789763:0.000000
():@0.226215:0.806586:0.247245:0.806586:0.247245:0.787099:0.226215:0.787099:0.000000:0.000000
+= −:@0.251233:0.813958:0.297273:0.813958:0.297273:0.798710:0.251233:0.798710:0.000000:0.000000:0.000000:0.000000
38:@0.216980:0.805384:0.240663:0.805384:0.240663:0.790634:0.216980:0.790634:0.000000:0.000000
4:@0.223381:0.824229:0.231475:0.824229:0.231475:0.809479:0.223381:0.809479:0.000000
4:@0.263566:0.814334:0.271660:0.814334:0.271660:0.799584:0.263566:0.799584:0.000000
2:@0.297201:0.814334:0.305294:0.814334:0.305294:0.799584:0.297201:0.799584:0.000000
(8, -2):@0.462352:0.814383:0.499157:0.814383:0.499157:0.799484:0.462352:0.799484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
12:@0.121173:0.848682:0.137523:0.848682:0.137523:0.833783:0.121173:0.833783:0.000000:0.000000
y:@0.179240:0.848663:0.185973:0.848663:0.185973:0.833938:0.179240:0.833938:0.000000
=:@0.190783:0.848290:0.199888:0.848290:0.199888:0.833042:0.190783:0.833042:0.000000
−:@0.204918:0.839343:0.214023:0.839343:0.214023:0.824095:0.204918:0.824095:0.000000
():@0.223200:0.840917:0.250681:0.840917:0.250681:0.821431:0.223200:0.821431:0.000000:0.000000
+= −:@0.254672:0.848290:0.300712:0.848290:0.300712:0.833042:0.254672:0.833042:0.000000:0.000000:0.000000:0.000000
312:@0.213964:0.839716:0.244630:0.839716:0.244630:0.824966:0.213964:0.824966:0.000000:0.000000:0.000000
4:@0.223633:0.858561:0.231727:0.858561:0.231727:0.843811:0.223633:0.843811:0.000000
4:@0.267019:0.848666:0.275113:0.848666:0.275113:0.833916:0.267019:0.833916:0.000000
5:@0.300653:0.848666:0.308747:0.848666:0.308747:0.833916:0.300653:0.833916:0.000000
(12, -5):@0.458264:0.848687:0.503245:0.848687:0.503245:0.833788:0.458264:0.833788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cción y expresión:@0.117728:0.090870:0.242599:0.090870:0.242599:0.075506:0.117728:0.075506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.096132:0.091656:0.108221:0.091656:0.108221:0.074520:0.096132:0.074520:0.000000