# How do you solve 6x-3y=4, -12x+6y=8 using the elimination method?

Oct 24, 2016

No solution is possible for this pair of equations.

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 6 x - 3 y = 4$
[2]$\textcolor{w h i t e}{\text{XXX}} - 12 x + 6 y = 8$

If we multiply equation [1] by $2$
so as to be able to eliminate the $x$ term from equation [2]
[3]$\textcolor{w h i t e}{\text{XXX}} 12 x - 6 y = 8$
then add equations [2] and [3]
[4]$\textcolor{w h i t e}{\text{XXX}} 0 = 16$
...an obviously impossible result.

The problem is that the given equations represent a pair of parallel lines which do not intersect and therefore have no solution point.