# How do you solve the following system: 6x + y = 2, 3x - 4y = -10?

##### 1 Answer
Mar 15, 2016

$x = - \frac{2}{27}$ and $y = \frac{22}{9}$

#### Explanation:

$6 x + y = 2$ ---------Eqn $1$
$3 x - 4 y = - 10$ ---------Eqn $2$

Multiplying Eqn $2$ by $2$

$6 x - 8 y = - 20$ ---------Eqn $3$

Subtracting Eqn $1$ from Eqn $3$
Note: Subtracting changes the bottom equation's sign

$\cancel{6 x} + y = 2$
$\cancel{- 6 x} + 8 y = 20$

$9 y = 22 \implies y = \frac{22}{9}$

put $y = \frac{22}{9}$ in Eqn $2$

$3 x - 4 \left(\frac{22}{9}\right) = - 10$

$3 x - \frac{88}{9} = - 10$

$27 x - 88 = - 90$

$27 x = - 90 + 88$

$27 x = - 2 \implies x = - \frac{2}{27}$