Question

Resolva os sistemas de equações

a){x+2y=6
{x-y=4

b){8x+2y=4
{x-y=10

c){3x+y=-5
{5x-2y=-1​

Answer 1

Resposta:

a){x+2y=6

{x-y=4

$x + 2y = 6 \\ x - y = 4 \\ \\ x + 2y = 6 \\ x = 4 + y \\ \\ 4 + y + 2y = 6 \\ 3y = 6 - 4 \\ 3y = 2 \\ y = \frac{2}{3} \\ \\ x = 4 + \frac{2}{3} \\ \\ x = \frac{14}{3} \\ \\ (x.y) = ( \frac{14}{3} . \frac{2}{3} )$

b){8x+2y=4

{x-y=10

$8x + 2y = 4 \\ x - y = 10 \\ \\ 8x + 2y = 4 \\ x = 10 + y \\ \\ 8 \times (10 + y) + 2y = 4 \\ 80 + 8y + 2y = 4 \\ 10y = 4 - 80 \\ 10y = - 76 \div (2) \\ 5y = - 38 \\ y = - \frac{38}{5} \\ \\ x = 10 + ( - \frac{38}{5} ) \\ \\ x = 10 - \frac{38}{5} \\ \\x = \frac{12}{5} \\ \\ (x.y) = ( \frac{12}{5} . - \frac{38}{5} )$

c){3x+y=-5

{5x-2y=-1

$3x + y = - 5 \\ 5x - 2y = - 1 \\ \\ y = - 5 - 3x \\ 5x - 2y = - 1 \\ \\ 5x - 2 \times ( - 5 - 3x) = - 1 \\ 5x + 10 + 6x = - 1 \\ 11x = - 1 - 10 \\ 11x = - 11 \div (11) \\ x = - 1 \\ \\ y = - 5 - 3x \\ y = - 5 - 3 \times ( - 1) \\ y = - 5 + 3 \\ y = \times 2 \\ \\ (x.y) = ( - 1. - 2)$