In order to solve a system of equations by elimination, we just have to combine (add or subtract) the equations and see if we can eliminate some variables.
By adding the first equation from the second equation we get:
As you can see, we got -3y = 27. By dividing by -3 on both sides of these expressions, we can solve for y to get:
-3y/-3 = 27/-3
y = -9
Then, y equals -9.
If we replace y into any of the two original equations, we should get the same result for x, let's use the first equation:
6x+2y=12
6x+2(-9)=12
6x - 18 = 12
6x = 12 + 18
6x = 30
x = 30/6
x = 5
Then, the system has a solution and it is (5, -9)