# How do you solve the system of equations: 6x-8y=2 and 9/2x-6y=3/2?

Aug 5, 2015

There is no unique solution to this pair of equations (they are the same equation except for a constant multiple)

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$6 x - 8 y = 2$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$\frac{9}{2} x - 6 y = \frac{3}{2}$

Simplify [2] by multiplying by 2
[3]$\textcolor{w h i t e}{\text{XXXX}}$$9 x - 12 y = 3$

Convert [1] and [3] so $y$ has equal coefficient values in both
Multiply [1] by 3
[4]$\textcolor{w h i t e}{\text{XXXX}}$$18 x - 24 y = 6$
Multiply [3] by 2
[5]$\textcolor{w h i t e}{\text{XXXX}}$$18 x - 24 y = 6$

Note that the equations are identical
$\textcolor{w h i t e}{\text{XXXX}}$(going back through the steps
$\textcolor{w h i t e}{\text{XXXX}}$we can see that [1] multiplied by $\frac{3}{4}$ is the same as [2]