10
QuizMultiple Choice

Solving Linear-Quadratic Systems — Quiz

Question 10 • Mathematics II

Which represents the solution(s) of the graphed system of equations, y is equal to x squared plus 2 x minus 3 and y is equal to x minus 1 ? Expand Image

Answer
A
0 comma negative 3 and 1 comma 0
B
negative 3 comma negative 2 and 0 comma 1
C
negative 2 comma negative 3 and 1 comma 0
D
1 comma 0 and 0 comma negative 1

Explanation

At an intersection, both equations have the same y-value, so set them equal: x² + 2x − 3 = x − 1. This gives x² + x − 2 = 0, which factors as (x + 2)(x − 1) = 0, so x = −2 or x = 1. Substituting into y = x − 1 gives the points (−2, −3) and (1, 0), which matches choice C.

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