To solve the system of equations:
2x - 6y = -12
x + 2y = 14
We can use the elimination method by multiplying the second equation by 2 so that the coefficient of x becomes the same as the coefficient of x in the first equation:
2x - 6y = -12
2x + 4y = 28
We can now subtract the first equation from the second equation to eliminate x:
2x + 4y - (2x - 6y) = 28 - (-12)
10y = 40
y = 4
Substituting y = 4 into the second equation, we get:
x + 2y = 14
x + 2(4) = 14
x + 8 = 14
x = 6
Therefore, the solution to the system of equations is x = 6 and y = 4.