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

Jun 6, 2015

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

Using [2] substitute $\left(- 3 x + 1\right)$ for $y$ in [1]
[3]$\textcolor{w h i t e}{\text{XXXX}}$$- x + \left(- 3 x + 1\right) = 5$
Simplifying
[4]$\textcolor{w h i t e}{\text{XXXX}}$$- 4 x = 4$
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x = - 1$

Using [5] substitute $\left(- 1\right)$ of $x$ in [1]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$- \left(- 1\right) + y = 5$
Simplifying
[7]$\textcolor{w h i t e}{\text{XXXX}}$$y = 4$

Solution is $\left(x , y\right) = \left(- 1 , 4\right)$