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

Mar 19, 2017

The solution is (4, 6).

Explanation:

Using substitution in this case means plugging in $x + 2$ for $y$ (for example), since they are stated to be equal.

$y = 2 x - 2 \textcolor{w h i t e}{\text{X" & color(white)"X}} y = x + 2$

Therefore, $2 x - 2 = x + 2$
$\textcolor{w h i t e}{\text{XXXXXXX-X}} 2 x = x + 4$
$\textcolor{w h i t e}{\text{XXXXXXXXX}} x = 4$

Now we know that $x = 4$, so plug in $x$ to one of the equations in order to find $y$.

$y = x + 2$
$y = 4 + 2$
$y = 6$

So, the solution is (4, 6).