# How do you solve 8x+5y=-4 and  -5x+y=19 using substitution?

May 26, 2016

(x,y)=color(blue)(""(-3,4))
(see below for solution using substitution).

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 8 x + 5 y = - 4$
[2]$\textcolor{w h i t e}{\text{XXX}} - 5 x + y = 19$

Note that [2] can be re-written as
[3]$\textcolor{w h i t e}{\text{XXX}} y = 5 x + 19$

We can therefore substitute $\left(5 x + 19\right)$ in place of $y$ in [1]
[4]$\textcolor{w h i t e}{\text{XXX}} 8 x + 5 \left(5 x + 19\right) = - 4$

[5]$\textcolor{w h i t e}{\text{XXX}} 33 x + 95 = - 4$

[6]$\textcolor{w h i t e}{\text{XXX}} 33 x = - 99$

[7]$\textcolor{w h i t e}{\text{XXX}} x = - 3$

We can now substitute $\left(- 3\right)$ in place of $x$ in [3]
[8]$\textcolor{w h i t e}{\text{XXX}} y = 5 \left(- 3\right) + 19$

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