What is the solution set of 4x=y and 2x^2-y=0

The equation 4x = y is solve for y so we can substitute the expression 4x for y in the other equation.

2x² - (4x) = 0 ← Substituted 4x for y...Hug'em when you plug'em (use ( )s)
2x² - 4x = 0 ← prepare to factor
2x(x - 2) = 0 ← factored out the GCF
2x = 0 or x - 2 = 0 ← zero product property
x = 0 or x = 2 ← solved each mini equation
If x = 0, then y = 4(0) = 0. (0, 0) is a solution
If x = 2, then y = 4(2) = 8. (2, 8) is a solution
The solution set is {(0,0), (2,8)}