David wants to find the solutions of this system of equations: –4x – 7 = yx2 – 2x – 6 = yWhich statement is true?There are no real number solutions.There is one unique real number solution at (–1, –3).There is one unique real number solution at (1, –3).There are two real number solutions at (–1, –3) and (1, –7).
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 two expressions for y equal: −4x − 7 = x² − 2x − 6. Rearranging gives x² + 2x + 1 = 0, or (x + 1)² = 0, so the only x-value is −1. Substituting it into y = −4x − 7 gives y = −3, so there is one unique real solution at (−1, −3).
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