# How do you solve the following system: -x+6y=12, 3x+4y=-10 ?

Sep 8, 2016

$x = - \frac{54}{11}$

$y = \frac{13}{11}$

#### Explanation:

$- x + 6 y = 12$ and $3 x + 4 y = - 10$

or

$x = 6 y - 12$

or

$x = 6 \left(y - 2\right)$

Multiplying $- x + 6 y = 12$ by $3$

We get

$- 3 x + 18 y = 36$

By adding $- 3 x + 18 y = 36$ with $3 x + 4 y = - 10$

We get

$- 3 x + 18 y + 3 x + 4 y = 36 - 10$

or

$22 y = 26$

or

$y = \frac{26}{22}$

or

$y = \frac{13}{11}$----------------------Ans $1$

By plugging the value $y = \frac{13}{11}$ in the equation $x = 6 \left(y - 2\right)$

We get

$x = 6 \left(\frac{13}{11} - 2\right)$

or

$x = 6 \times \frac{13 - 22}{11}$

or

$x = 6 \times \left(- \frac{9}{11}\right)$

or

$x = - \frac{54}{11}$---------------------Ans $2$