Question

Which is a solution to the following system of equations?



⎧
⎨
⎩
y
=
−
x
2
y
=
−
1
8
x


(
0,0
)


(
−
1
,
−
1
)


(
1
,
−
1
8
)


There is no solution.

Answer 1

Set -x^2 = -(1/8)x. Multiply by 8: -8x^2 + x = 0 → x( -8x + 1 ) = 0, so x = 0 or x = 1/8.
For x = 0, y = 0 → (0,0). For x = 1/8, y = -(1/8)(1/8) = -1/64 (not one of the choices).
Thus the solution from the choices is (0,0).