Question

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

Answer 1

No solution is possible for this pair of equations.

Explanation:

Given
[1]`color(white)("XXX")6x-3y=4`
[2]`color(white)("XXX")-12x+6y=8`

If we multiply equation [1] by `2`
so as to be able to eliminate the `x` term from equation [2]
[3]`color(white)("XXX")12x-6y=8`
then add equations [2] and [3]
[4]`color(white)("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.