Question

Which of the following graphs represents the solution(s) of the following system?
x2 – y = –2
4y – 8 = x

Answer 1

Interpreting x2 as x^2, the system is
x^2 − y = −2 and 4y − 8 = x.

Rewrite each as y =:
y = x^2 + 2 (parabola, vertex (0,2))
y = x/4 + 2 (line, slope 1/4, y‑intercept 2)

Set equal: x^2 + 2 = x/4 + 2 ⇒ x^2 = x/4 ⇒ x(x − 1/4) = 0,
so x = 0 or x = 1/4. The corresponding points are
(0, 2) and (1/4, 33/16) (33/16 = 2.0625).

So the correct graph shows the upward parabola y = x^2 + 2 and the shallow line y = x/4 + 2 intersecting at (0,2) and (1/4,33/16).