# How do you solve the following system?: 9x -5y =21, -x -y = -2

Jun 27, 2018

$\left(\frac{31}{14} , - \frac{3}{14}\right)$

#### Explanation:

Let's start with the second equation by dividing every term by $- 1$. We now have the following system:

$\textcolor{b l u e}{9 x - 5 y = 21}$

$x + y = 2$

Let's subtract $x$ from both sides of the second equation. We get

$\textcolor{red}{y = - x + 2}$

We can now plug this value into the blue equation. We get

$9 x - 5 \textcolor{b l u e}{\left(- x + 2\right)} = 21$

Simplifying gives us

$9 x + 5 x - 10 = 21$

$\implies 14 x = 31$

$\implies x = \frac{31}{14}$

We can plug this into the red equation to get

$y = - \textcolor{red}{\frac{31}{14}} + \frac{28}{14}$

$y = - \frac{3}{14}$

Therefore, our solutions are

$\left(\frac{31}{14} , - \frac{3}{14}\right)$

Hope this helps!