Question

Determine o valor de y no sistema: x + y = 7 x – 2y = – 5 *

Por favor me ajudemmmm

Answer 1

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

Regra de Cramer:

$d = | \frac{1}{7} \frac{1}{ - 2} | = - 9 \\ |d| = 1 \times ( - 2) - \times 7 \\ |d| = - 2 - 7 \\ |d| = - 9 \\ d _{1} = | \frac{ - 5}{ - 5} \frac{1}{ - 2} | \\ |d(1)| = - 5 \times ( - 2) - 1 \times ( - 5) \\ |d(1)| = 5 \times 2 + 1 \times 5 \\ |d(1)| = 15 \\ d _{2} = | \frac{1}{7} \frac{ - 5}{ - 5} \\ | |d(2)| = 1 \times ( - 5) - ( - 5) \times 7 \\ |d(2)| = - 5 + 5 \times 7 \\ |d (2)| = 30$

$x = \frac{d_{1}}{d} \\ y = \frac{d_{2}}{d}$

Substituindo:

$x = - \frac{5}{3} \\ \pink{y = - \frac{ 10}{3}}$

$(x,y) = ( - \frac{5}{3} , - \frac{10}{3})$