# How do you solve 2x+2y=14 and 2x-y=5 using substitution?

Apr 8, 2016

$x = 4 , y = 3$

#### Explanation:

First you want to find a definition for either $x$ or $y$ in terms of the other, using the second equation.

$2 x - y = 5$
$2 x = y + 5$
$y = 2 x - 5$

Now you can substitute this into the first equation.

$2 x + 2 y = 14$
$2 x + 2 \left(2 x - 5\right) = 14$
$6 x - 10 = 14$
$6 x = 24$
$x = 4$

With this value, substitute into anything and it should give you $y$. Lets use the direct equation for $y$ we found.

$y = 2 x - 5$
$y = 2 \cdot 4 - 5$
$y = 3$

You can substitute these values into any of the equations and they should work, if they are correct.