What is the solution set of 4x = y and 2x2 − y = 0? {(0.5, -0.5), (2, -8)} {(0, 0), (2, 8)} {(1.5, 2), (8, 2)} {(-1.5, -2), (2, 8)}

Solve the system 

4x = y
2x^2 − y = 0             (Note:  Use " ^ " to denote exponentiation.)

In the 2nd equation, subst. 4x for y:  2x^2 - (4x) = 0.  Then,

2x^2 - 4x = 0.  Factor out one x:    x(2x - 4) = 0.  This produces two roots, which are {0, 2}.

Next, find y.  y=4x.  So, if x: {0, 2},   we get   y: {0, 8}

Roots may be (0,0) and (2,8).  It's important that you check your results by subst. their x- and y-coordinates into the original equations.