# How do you solve x-2y=2 and y= -1/2x-5?

Nov 6, 2015

$x = 6 \mathmr{and} y = - 8$ through systems of equations.

#### Explanation:

This is known as a system of equations. For this system, we are going to use substitution, since you already know what y is equal to.

As you can see, $y = - \frac{1}{2} x - 5$. Since we have $y$ directly set equal to something, we can substitute it in for $y$ anywhere we want. In this case we will substitute it in for $y$ in your first equation. $x - 2 y = 2 \implies x - 2 \left(- \frac{1}{2} x - 5\right) = 2$

Through algebraic equation steps, we can simplify the equation to be $x + x - 10 = 2$, and solve the equation for $x = 6$.

Now that we have the $x$ value, we can substitute it in to the $y$ equation.
$y = - \frac{1}{2} \left(6\right) - 5$

When simplified, you get $y = - 3 - 5$, or $y = - 8$. And remember, if you'd like to check your answer, simply plug your numbers back in for the variables.

$y = - \frac{1}{2} x - 5 \implies \left(- 8\right) = - \frac{1}{2} \left(6\right) - 5$, and when simplified, $- 8 = - 8$.