To solve this system of equations, we can use either substitution or elimination method. Here's how to solve it using substitution:
Substitute the expression for y from the first equation into the second equation, and solve for x:
4x - 2(-2x + 8) = 8
4x + 4x - 16 = 8
8x = 24
x = 3
Now substitute this value of x back into the first equation to find y:
y = -2x + 8
y = -2(3) + 8
y = 2
Therefore, the solution to the system of equations is (x, y) = (3, 2).
To check this solution, we can substitute the values of x and y back into the original equations:
y = -2x + 8
2 = -2(3) + 8
2 = 2 (this checks out)
4x - 2y = 8
4(3) - 2(2) = 8
12 - 4 = 8 (this also checks out)
So our solution is correct.