# How do you solve the system 2x+2y=7 and x-2y=-1 using substitution?

Nov 9, 2016

$y = \frac{3}{2}$ and $x = 2$

#### Explanation:

Step 1) Solve the second equation for $x$ while keeping the equation balanced:

$x - 2 y + 2 y = - 1 + 2 y$

$x = 2 y - 1$

Step 2) Substitute $2 y - 1$ for $x$ in the first equation and solve for $y$ while keeping the equation balanced.

$2 \left(2 y - 1\right) + 2 y = 7$

$4 y - 2 + 2 y = 7$

$6 y - 2 = 7$

$6 y - 2 + 2 = 7 + 2$

$6 y = 9$

$\frac{6 y}{6} = \frac{9}{6}$

$y = \frac{3}{2}$

Step 3) Substitute $\frac{3}{2}$ for $y$ in the second equation and solve for $x$ while keeping the equation balanced:

$x = 2 \left(\frac{3}{2}\right) - 1$

$x = 3 - 1$

$x = 2$