Question

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)}

Answer 1

{(0, 0), (2, 8)}

Explanation:

Answer 2

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.