# How do you find the solution of the system of equations x-2y=2 and y= -1/2x-5?

Jun 15, 2018

$x = - 4$
$y = - 3$

#### Explanation:

The second equation gives an expression for $y$ in terms of $x$:

$y = - \frac{1}{2} x - 5$

This means that we can substitute the $y$ in the first equation with that expression:

$x - 2 \textcolor{red}{y} = 2 \setminus \to x - 2 \setminus \textcolor{red}{\left(- \frac{1}{2} x - 5\right)} = 2$

Rearrange this last expression:

$x + x + 10 = 2 \setminus \to 2 x + 10 = 2$

Subtract $10$ from both sides:

$2 x = - 8$

Divide both sides by $2$:

$x = - 4$

Now that we know $x$, we can use the expression for $y$ to find it out:

$y = - \frac{1}{2} \setminus \textcolor{red}{x} - 5 = - \frac{1}{2} \setminus \textcolor{red}{\left(- 4\right)} - 5 = 2 - 5 = - 3$