# How do you solve x = -5 + 2y and 2x + 3y = 4 using substitution?

Aug 5, 2016

To solve, substitute the $x$ in the second equation for the $x$ in the first equation.

#### Explanation:

The first equation is already solved for $x$, so let's put that equation into the second equation. It'll look like this:

$2 \left(- 5 + 2 y\right) + 3 y = 4$

Next, use the distributive property to simplify our equation:

$- 10 + 4 y + 3 y = 4$

Now, let's combine $3 y$ and $4 y$ to make $7 y$:

$- 10 + 7 y = 4$

Next, add $10$ to each side:

$7 y = 14$

The final step in solving for y is to divide each side by $7$:

$y = 2$

We've now solved for y. Now, we have to solve for x. The easiest way to do this is to substitute our y-value into the first equation, since it's already solved for x:

$x = - 5 + 2 \left(2\right)$

$x = - 5 + 4$

$x = - 1$

Using our x and y value and combining them to get an ordered pair, we now have our answer: $\left(- 1 , 2\right)$