84314
AssignmentMultiple Choice

Solving Linear-Quadratic Systems

Question 84314 • Algebra III A

David wants to find the solutions of this system of equations: –4x – 7 = yx2 – 2x – 6 = yWhich statement is true?

Answer
A
There are no real number solutions.
B
There is one unique real number solution at (–1, –3).
C
There is one unique real number solution at (1, –3).
D
There are two real number solutions at (–1, –3) and (1, –7).

Explanation

Set the expressions for y equal: −4x − 7 = x² − 2x − 6. Rearranging gives (x + 1)² = 0, so x = −1; substituting into y = −4x − 7 gives y = −3. Thus the system has one unique real solution, (−1, −3), which is choice B.

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