# How do you solve by substitution: y=-x+5 and 3x-y=-1?

Oct 1, 2015

Substitute the expression given for $y$ by the first equation for $y$ in the second equation and simplify to get
#(x,y)=(1,4)

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXX}} y = - x + 5$
[2]$\textcolor{w h i t e}{\text{XXX}} 3 x - y = - 1$

Substituting $\left(- x + 5\right)$ from [1] into $\left[2\right]$ in place of $y$
[3]$\textcolor{w h i t e}{\text{XXX}} 3 x - \left(- x + 5\right) = - 1$

Simplifying
[4]$\textcolor{w h i t e}{\text{XXX}} 4 x - 5 = - 1$

[5]$\textcolor{w h i t e}{\text{XXX}} 4 x = 4$

[6]$\textcolor{w h i t e}{\text{XXX}} x = 1$

Substituting $1$ for $x$
[7]$\textcolor{w h i t e}{\text{XXX}} y = - 1 + 5$

[8]$\textcolor{w h i t e}{\text{XXX}} y = 4$