Question

1) Resolva o sistema de equaçao método da adição
A) {x- y = 2
x + y = 12

B) {3x + 5y =11
5x - 5y = 5

Answer 1

A)
$x - y = 2 \\ x + y = 12 \\ \\ (x + x) - ( - y + y) = (2 + 12) \\ 2x + y - y = 14 \\ 2x = 14 \\ x = \frac{14}{2} \\ x = 7 \\ \\ x - y = 2 \\ 7 - y = 2 \\ - y = 2 - 7 \\ - y = - 5 \\ - y \times ( - 1) = - 5 \times ( - 1) \\ y = 5 \\ x = 7$

B)
$3x + 5y = 11 \\ 5x - 5y = 5 \\ \\ (3x + 5y) - ( 5y - 5y) = 11 + 5 \\ 8x - 5y + 5y = 16 \\ 8x = 16 \\ x = \frac{16}{8} \\ x = 2 \\ \\ 3x + 5y = 11 \\ 3 \times 2 + 5y = 11 \\ 6 + 5y = 11 \\ 5y = 11 - 6 \\ 5y = 5 \\ y = \frac{5}{5} \\ y = 1 \\ \\ x = 2 \\ y = 1$