# How do you solve the system of equations 4x - 5y = - 7 and 4x + 5y = - 17?

Jun 21, 2017

color(purple)(y=-1,x=-3

#### Explanation:

$4 x - 5 y = - 7 - - - - \left(1\right)$

$4 x + 5 y = - 17 - - - - \left(2\right)$

$\therefore \left(1\right) - \left(2\right)$

$\therefore - 10 y = 10$

$\therefore y = \frac{10}{-} 10$

:.color(purple)(y=-1

Substitute y=-1 in (1)

$\therefore 4 x - 5 \left(\textcolor{p u r p \le}{- 1}\right) = - 7$

$\therefore 4 x + 5 = - 7$

$\therefore 4 x = - 7 - 5$

$\therefore 4 x = - 12$

$\therefore x = - \frac{12}{4}$

:.color(purple)(x=-3

Check:

Substitute color(purple)(y=-1 , x=-3 in (1)

$\therefore 4 \left(\textcolor{p u r p \le}{- 3}\right) - 5 \left(\textcolor{p u r p \le}{- 1}\right) = - 7$

$\therefore - 12 + 5 = - 7$

:.color(purple)(-7=-7