# How do you solve the following system: 5x-2y=-26, 6x + 7y = -9 ?

Apr 8, 2018

$x = - \frac{200}{47}$ and $y = \frac{111}{47}$

#### Explanation:

5x - 2y = -26 color(white)(..)……(1)
6x + 7y = -9 color(white)(..) ……(2)

Multiply equation $\left(1\right)$ by $7$ and equation $\left(2\right)$ by $2$

$35 x - 14 y = - 182$
$12 x + 14 y = - 18$

$35 x - 14 y + 12 x + 14 y = - 182 - 18$

$47 x = - 200$

color(blue)(x = -200/47

Substitute $x = - \frac{200}{47}$ in equation $\left(1\right)$

$5 \left(- \frac{200}{47}\right) - 2 y = - 26$

$- \frac{1000}{47} - 2 y = - 26$

$2 y = - \frac{1000}{47} + 26$

2y = -1000/47 + (26 × 47/47)

$2 y = - \frac{1000}{47} + \frac{1222}{47}$

$2 y = \frac{- 1000 + 1222}{47}$

$2 y = \frac{222}{47}$

y = 222/(2 × 47)

$\textcolor{b l u e}{y = \frac{111}{47}}$