Question

Using the substitution method, which of
the following options is the correct
solution for the linear-quadratic system
y = x − 4x − 41, ? (1 point)
2 y = 4
(5, 4) and (−9, 4)
(9, 4)
(−5, 4)
(−5, 4) and (9, 4)

Answer 1

Interpret the system as
y = x^2 − 4x − 41
y = 4

Substitute y = 4 into the quadratic:
4 = x^2 − 4x − 41
0 = x^2 − 4x − 45
0 = (x − 9)(x + 5)

So x = 9 or x = −5, giving the solution pairs (9, 4) and (−5, 4).

Answer: (−5, 4) and (9, 4).