# How do you solve the following equations by substitution: 8x - 4y = 16 and y = 2x - 4??

Oct 21, 2015

There are infinitely many solutions to this pair of equations. (See below for demonstration using substitution).

#### Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXX}} 8 x - 4 y = 16$
[2]$\textcolor{w h i t e}{\text{XXX}} y = 2 x - 4$

Substituting $\left(2 x - 4\right)$ from [2] for $y$ in [1]
[3]$\textcolor{w h i t e}{\text{XXX}} 8 x - 4 \left(2 x - 4\right) = 16$

Simjplifying
[4]$\textcolor{w h i t e}{\text{XXX}} 16 = 16$

Since this is true for all pairs $\left(x , y\right)$ there is no unique solution.
(The equations represent the same line).