# How do you solve by substitution 4x-7y=10 and y= x-7?

Jun 4, 2015

Given
[1]$\textcolor{w h i t e}{\text{XXXX}}$$4 x - 7 y = 10$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$y = x - 7$

Using [2] substitute $\left(x - 7\right)$ for $y$ in [1]
[3]$\textcolor{w h i t e}{\text{XXXX}}$$4 x - 7 \left(x - 7\right) = 10$

Simplifying
[4]$\textcolor{w h i t e}{\text{XXXX}}$$- 3 x + 49 = 10$
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x = 13$

Using [5] substitute $\left(13\right)$ for $y$ in [2]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = \left(13\right) - 7$
[7]$\textcolor{w h i t e}{\text{XXXX}}$$y = 6$

$\left(x , y\right) = \left(13 , 6\right)$