# How do you solve the following system using substitution?: x=4-4y, -x+2y=2

Nov 5, 2015

y = 1
x=0

#### Explanation:

First replace all values of x in the second equation with $4 - 4 y$ (this can be done for y as well but you would need to isolate the variable first)

Which gives you:
$- \left(4 - 4 y\right) + 2 y = 2$

Then solve using algebra:
Distribute the $-$
$- 4 + 4 y + 2 y = 2$

Combine all all the y values
$- 4 + 6 y = 2$

$\left(- 4 + 6 y\right) + 4 = \left(2\right) + 4 \rightarrow 6 y = 6$

Finally divide both sides by 6
$\frac{6 y}{6} = \frac{6}{6} \rightarrow y = 1$

Thus your y value is equal to 1. To find the x value, substitute this 1 into one of the equations for all y's
$x = 4 - 4 \left(1\right)$

Then simplify
$x = 4 - 4 \rightarrow x = 0$

thus x is equal to 0

You could also check your answer by substituting both values into the other equation
$- \left(0\right) + 2 \left(1\right) = 2$

$0 + 2 = 2$

$2 = 2$