Question

Resolva os sistemas abaixo:
a) {x+y=7
{2x-y=-1

b) {x+2y=5
{2x+y=-2

c) {-2x+y=-6
{-3x-y=1​

Answer 1

Resposta:

a) x = 2; y = 5;

b) x = -3; y = 4;

c) x = 1; y = -4;

Explicação passo a passo:

a)

$\left \{ {{x+y=7} \atop {2x-y=-1}} \right.$

Utilizando o método da adição:

$x+2x+y-y=7-1\\\\3x=6\\\\x=\frac{6}{3}\\ \\x=2$

Para x = 2:

$x+y=7\\\\2+y=7\\y=5$

b)

$\left \{ {{x+2y=5} \atop {2x+y=-2}} \right.$

Multiplicando ambos os membros da segunda equação por (-2) temos:

$2x*(-2)+y*(-2)=-2*(-2)\\\\-4x-2y=4\\\\\\\left \{ {{x+2y=5} \atop {-4x-2y=4}} \right.$

Utilizando o método da adição:

$x-4x+2y-2y=5+4\\\\-3x=9\\\\x=-\frac{9}{3} \\\\x=-3$

Para x = -3:

$2x+y=-2\\\\2*(-3)+y=-2\\\\-6+y=-2\\\\y=-2+6\\\\y=4$

c)

$\left \{ {{-2x+y=-6} \atop {-3x-y=1}} \right.$

Utilizando o método da adição:

$-2x-3x+y-y=-6+1\\\\-5x=-5\\\\x=\frac{-5}{-5}\\ \\x=1$

Para x = 1:

$-2x+y=-6\\\\-2*(1)+y=-6\\\\-2+y=-6\\\\y=-6+2\\\\y=-4$

Answer 2

Olá

a)

$\sf \huge \left \{ {{x + y=7} \atop {2x - y= - 1}} \right. \\ \\ \sf \huge \left \{ {{y=7 - x} \atop {2x -(7 - x) = - 1}} \right. \\ \\ \sf \huge \: 2x - (7 - x) = - 1 \\ \sf \huge \: 2x - 7 + x = - 1 \\ \sf \huge \: 3x -7 = - 1 \\ \sf \huge \: 3x = - 1 + 7 \\ \sf \huge \: 3x = 6 \\ \sf \huge \: x = \frac{6}{3} \\ \\ \huge {\boxed {\blue { \sf x= 2} }} \\ \\ \\ \sf \huge \: y = 7 - 2 \\ \\ \huge {\boxed {\blue { \sf y= 5} }} \\ \\ \huge {\boxed {\blue { \sf (x ,y) =(2 ,5) } }}$

b)

$\sf \huge \left \{ {{x + 2y=5} \atop {2x + y= - 2}} \right. \\ \\ \sf \huge \left \{ {{x=5 - 2y} \atop {2(5 - 2y) +y= - 2}} \right. \\ \\ \sf \huge \: 10-4y +y= - 2 \\ \sf \huge \: 10 - 3y = - 2\\ \sf \huge \: -3y = - 2-10 \\ \sf \huge \: -3y = - 12 \\ \\ \huge {\boxed {\green { \sf y= 4} }} \\ \\ \\ \sf \huge \: x = 5 - 2.4 \\ \\ \huge {\boxed {\green { \sf x= -3 } }} \\ \\ \huge {\boxed {\green { \sf (x ,y) =(-3 ,4) } }}$

c)

$\sf \huge \left \{ {{-2x + y=-6} \atop {-3x - y= 1}} \right. \\ \\ \sf \huge \left \{ {{y=-6 + 2x} \atop {-3x-(-6 + 2x) = 1}} \right. \\ \\ \sf \huge \: -3x +6 - 2x = 1 \\ \sf \huge \: -5x + 6 = 1 \\ \sf \huge \: -5x = 1-6\\ \sf \huge \: -5x = - 5 \\ \sf \huge \: x = \frac{-5}{-5} \\ \\ \huge {\boxed {\red { \sf x= 1} }} \\ \\ \\ \sf \huge \: y = -6 + 2 \\ \\ \huge {\boxed {\red { \sf y= -4} }} \\ \\ \huge {\boxed {\red { \sf (x ,y) =(1 ,-4) } }}$