Question

Resolva o sistema de equação a seguir:
{x-y/2 - x-2/4 = y+1/3 - 1
{x-1/2 - y-3/3 = x+y/4 - 1/6

Por favor galera me ajude,estou quebrando a cabeça..

Answer 1

$\left \{ {{ \frac{x-y}{2} - \frac{x-2}{4} = \frac{y+1}{3} -1} \atop { \frac{x-1}{2}- \frac{y-3}{3} = \frac{x+y}{4}- \frac{1}{6} }} \right. \\ \\ \left \{ {{12. \frac{x-y}{2} -12. \frac{x-2}{4} =12. \frac{y+1}{3} -12.1} \atop { 12.\frac{x-1}{2}- 12.\frac{y-3}{3} =12. \frac{x+y}{4}- 12.\frac{1}{6} }} \right. \\ \\ \left \{ {{6(x-y)-3(x-2)=4(y+1)} -12\atop {6(x-1)-4(y-3)=3(x+y)-2}} \right. \\ \\ \left \{ {{6x-6y-3x+6=4y+4-12} \atop {6x-6-4y+12=3x+3y-2}} \right.$

$\left \{ {{6x-6y-3x-4y=4-12-6} \atop {6x-4y-3x-3y=6-12-2}} \right. \\ \\ \left \{ {{3x-10y=-14} \atop {3x-7y=-8}} \right. \\ \\ \left \{ {{-3x+10y=14} \atop {3x-7y=-8}} \right.$

Somando as duas equações

$-3x+3x+10y-7y=14-8 \\ \\ 3y=6 \\ \\ y= \frac{6}{3} \\ \\ y=2$

Substituindo y na equação 3x-10y=-14

$3x-10.2=-14 \\ \\ 3x-20=-14 \\ \\ 3x=-14+20 \\ \\ 3x=6 \\ \\ x= \frac{6}{3} \\ \\ x=2$

S={2,2}