# How do you solve the following system?: -5x -4y =3, 3x -y = -2

Mar 2, 2017

$x = - \frac{11}{17}$ and $y = \frac{1}{17}$

#### Explanation:

$- 5 x - 4 y = 3$
$3 x - y = - 2$

From the second equation, we can determine a temporary value for $y$.

$3 x - y = - 2$

Add $y$ to each side.

$3 x = y - 2$

Add $2$ to each side.

$3 x + 2 = y$

In the first equation, substitute $y$ with $\textcolor{red}{\left(3 x + 2\right)}$.

$- 5 x - 4 y = 3$

$- 5 x - 4 \textcolor{red}{\left(3 x + 2\right)} = 3$

Open the brackets ad simplify. The product of a negative and a positive is a negative.

$- 5 x - 12 x - 8 = 3$

$- 17 x - 8 = 3$

Add $8$ to each side.

$- 17 x = 11$

Divide both sides by $- 17$.

$x = - \frac{11}{17}$

In the second equation, substitute $x$ with $\textcolor{b l u e}{\left(- \frac{11}{17}\right)}$.

$3 x - y = - 2$

$3 \textcolor{b l u e}{\left(- \frac{11}{17}\right)} - y = - 2$

Open the brackets and simplify. The product of a positive and a negative is a negative.

$- \frac{33}{17} - y = - 2$

Add $y$ to each side.

$- \frac{33}{17} = y - 2$

Add $2$ to each side.

$- \frac{33}{17} + 2 = y$

$- \frac{33}{17} + \left(2 \times \frac{17}{17}\right) = y$

$- \frac{33}{17} + \frac{34}{17} = y$

$\frac{- 33 + 34}{17} = y$

$\frac{1}{17} = y$