# How do you solve the following system?:  3x+3y= -7 , 4x-y=-27

Feb 16, 2016

The solution for the system of equations is:

$x = \frac{- 88}{15}$

$y = \frac{53}{15}$

#### Explanation:

$3 x + \textcolor{b l u e}{3 y} = - 7$......equation $1$

$4 x - y = - 27$, multiplying by $3$
$12 x - \textcolor{b l u e}{3 y} = - 81$.....equation $2$

Solving by elimination

Adding equations $1$ and $2$:

$3 x + \cancel{\textcolor{b l u e}{3 y}} = - 7$

$12 x - \cancel{\textcolor{b l u e}{3 y}} = - 81$

$15 x = - 88$

$x = \frac{- 88}{15}$

Finding $y$ from equation $1$:
$3 x + 3 y = - 7$

$\cancel{3} \times \left(- \frac{88}{\cancel{15}}\right) + 3 y = - 7$

$\left(- \frac{88}{5}\right) + 3 y = - 7$
$3 y = - 7 + \frac{88}{5}$

$3 y = - \frac{35}{5} + \frac{88}{5}$

$3 y = \frac{53}{5}$

$y = \frac{53}{15}$