# How do you solve 2x+3y=6 and y=2x-6 using substitution?

May 15, 2016

(x,y)=color(blue)(""(3,0))
(see below for solution by substitution)

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 2 x + 3 y = 6$
[2]$\textcolor{w h i t e}{\text{XXX}} y = 2 x - 6$

Since from [2] we have that $y = 2 x - 6$
we can replace $y$ with $\left(2 x - 6\right)$ in [1]
to get
[3]$\textcolor{w h i t e}{\text{XXX}} 2 x + 3 \left(2 x - 6\right) = 6$

Simplifying
[4]$\textcolor{w h i t e}{\text{XXX}} 8 x - 18 = 6$

[5]$\textcolor{w h i t e}{\text{XXX}} \rightarrow 8 x = 24$

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

Since from [6] $x = 3$
we can replace $x$ with $\left(3\right)$ in [2]
to get
[7]$\textcolor{w h i t e}{\text{XXX}} y = 2 \left(3\right) - 6$

and simplifying
[8]$\textcolor{w h i t e}{\text{XXX}} y = 0$