# How do you solve -2x + y = 1 and -4x + y = -1 using substitution?

Apr 8, 2016

$\left(x , y\right) = \left(\textcolor{c y a n}{1 , 3}\right)$

#### Explanation:

If
$\textcolor{w h i t e}{\text{XXX}} - 2 x + y = 1$
then
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{y} = \textcolor{b l u e}{1 + 2 x}$

Since we are also told that
$\textcolor{w h i t e}{\text{XXX}} - 4 x + \textcolor{red}{y} = - 1$
we can substitute $\left(\textcolor{b l u e}{1 + 2 x}\right)$ for $\textcolor{red}{y}$ to get
$\textcolor{w h i t e}{\text{XXX}} - 4 x + \left(\textcolor{b l u e}{1 + 2 x}\right) = - 1$

$\textcolor{w h i t e}{\text{XXX}} - 2 x + 1 = - 1$

$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{x} = \textcolor{b r o w n}{1}$

Then substituting $\left(\textcolor{b r o w n}{1}\right)$ for $\textcolor{g r e e n}{x}$
in the original $- 2 \textcolor{g r e e n}{x} + y = 1$

$\textcolor{w h i t e}{\text{XXX}} - 2 \cdot \left(\textcolor{b r o w n}{1}\right) + y = 1$

$\textcolor{w h i t e}{\text{XXX}} - 2 + y = 1$

$\textcolor{w h i t e}{\text{XXX}} y = 3$