# How do you solve 9x - y = 317 and 10x - 11y = 550 using substitution?

Jun 9, 2016

(x,y)=color(green)(""(33,-20))
(see below for solution by substitution)

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 9 x - y = 317$
[2]$\textcolor{w h i t e}{\text{XXX}} 10 x - 11 y = 550$

We can re-arrange [1] as
[3]$\textcolor{w h i t e}{\text{XXX}} y = 9 x - 317$

Using [3] we can substitute $9 x - 317$ for $y$ in [2]
[4]$\textcolor{w h i t e}{\text{XXX}} 10 x - 11 \left(9 x - 317\right) = 550$

[5]$\textcolor{w h i t e}{\text{XXX}} 10 x - 99 x = 550 - 3487$

[6]$\textcolor{w h i t e}{\text{XXX}} 89 x = 2937$

[7]$\textcolor{w h i t e}{\text{XXX}} x = 33$

Using [7] we can substitute $33$ for $x$ in [1]
[8]$\textcolor{w h i t e}{\text{XXX}} 9 \left(33\right) - y = 317$

[9]$\textcolor{w h i t e}{\text{XXX}} 297 - y = 317$

[10]$\textcolor{w h i t e}{\text{XXX}} y = - 20$