# How do you solve the system 5x - y = - 14 + 2x + y and 7x + 9y + 4 = 3x + 8y?

Feb 6, 2017

$x = - 2$ and $y = 4$

#### Explanation:

First simplify both equations:
$5 x - y = - 14 + 2 x + y$

Subtract $2 x$ and $y$ from both sides.

$3 x - 2 y = - 14$

$\textcolor{red}{7 x + 9 y + 4 = 3 x + 8 y}$

Subtract $3 x$ and $8 y$ from both sides.

$\textcolor{red}{4 x + y + 4 = 0}$

Subtract $4$ from each side.

$\textcolor{red}{4 x + y = - 4}$

So now we have two simplified equations:
$3 x - 2 y = - 14$
$\textcolor{red}{4 x + y = - 4}$

Using the second equation, determine a value for $y$.

$\textcolor{red}{4 x + y = - 4}$

Subtract $4 x$ from both sides.

$\textcolor{red}{y = - 4 - 4 x}$

In the first equation, substitute $y$ with $\textcolor{red}{\left(- 4 - 4 x\right)}$.

$3 x - 2 y = - 14$

$3 x - 2 \textcolor{red}{\left(- 4 - 4 x\right)} = - 14$

Open the brackets and simplify. The product of two negatives results in a positive.

$3 x + \textcolor{red}{8 + 8 x} = - 14$

$11 x + 8 = - 14$

Subtract $8$ from each side.

$11 x = - 22$

Divide both sides by $11$.

$x = - 2$

In the second equation, substitute $x$ with $\textcolor{b l u e}{- 2}$.

$\textcolor{red}{4 x + y = - 4}$

$\textcolor{red}{4 \textcolor{b l u e}{\left(- 2\right)} + y = - 4}$

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

$\textcolor{red}{- 8 + y = - 4}$

Add $8$ to both sides.

$\textcolor{red}{y = 4}$