# How do you solve 2x + y = 1 and 4x + 2y = -2 using substitution?

May 19, 2017

Solve the first equation for $y$ and put it into the second equation.

#### Explanation:

We're going to have to plug one equation into the other if we want to solve for $x$ and $y$. First, we'll take the first equation and subtract $2 x$ from each side so that the equation is written in terms of $y$:

$y = - 2 x + 1$

Next, we substitute the $y$ in the second equation with the first equation and solve for $x$:

$4 x + 2 \left(2 x + 1\right) = - 2$
$4 x + 4 x + 2 = - 2$
$8 x + 2 = - 2$
$8 x = - 4$
$x = - \frac{1}{2}$

To solve for $y$, let's take our first equation and plug in our answer for $x$:

$y = - 2 \left(- \frac{1}{2}\right) + 1$
$y = 1 + 1$
$y = 2$