# How do you solve the following system?: -2x -3y =15, -3x +y = -17

Apr 21, 2016

The solution for the system of equations is:

$x = \frac{36}{11}$

$y = - \frac{79}{11}$

#### Explanation:

$- 2 x \textcolor{b l u e}{- 3 y} = 15$..................equation $\left(1\right)$

$- 3 x + y = - 17$, multiplying by $3$
$- 9 x + \textcolor{b l u e}{3 y} = - 51$.............equation $\left(2\right)$

Solving by elimination:

Adding both the equations eliminates $\textcolor{b l u e}{3 y} :$

$- 2 x \cancel{\textcolor{b l u e}{- 3 y}} = 15$
$- 9 x + \cancel{\textcolor{b l u e}{3 y}} = - 51$

$- 11 x = - 36$

$x = \frac{- 36}{- 11}$

$x = \frac{36}{11}$

Finding $y$ from equation $1$:
$- 2 x - 3 y = 15$

$- 2 x - 15 = 3 y$

$- 2 \cdot \left(\frac{36}{11}\right) - 15 = 3 y$

$- \frac{72}{11} - 15 = 3 y$

$- \frac{72}{11} - \frac{165}{11} = 3 y$

$- \frac{237}{11} = 3 y$

$- \frac{237}{11 \cdot 3} = y$

$y = - \frac{79}{11}$