Question

Solve the following system using the elimination method:
-3x + 4y = 6
9x - 12y = -18

Answer 1

By using elimination method, one of the variables must be eliminated by adding the two equations.
-3x + 4y = 6
9x - 12y = -18
We first choose the variable we want to eliminate. In here, let's choose x. To eliminate x, the term with variable x must have the same numerical coefficient (number before the variable) but have different signs (so that they would cancel). Thus, we multiply the first equation by 3:
3*(-3x + 4y) = 3*6
-9x + 12y = 18
Then we add the two equations:
-9x + 12y = 18
9x - 12y = -18
---------------------
0 + 0 = 0

Note that when you come up with this situation, this only means that the two lines are coinciding, meaning the solution is INFINITE. If however, the value of the constant (right side of equation) is not equal to zero, the lines are parallel and there is no solution.

Hope this helps~ :)