PSAT Math Multiple-Choice Question 826: Answer and Explanation
Question: 826
What are the possible values of b in the system of equations below?
b = 2a + 1
b + 2 = a2
- A. -3, -7
- B. -1, 7
- C. 3, -1
- D. 3, 7
Correct Answer: B
Explanation:
(B) Use substitution to solve for a:
b = 2a + 1 and b + 2 = a2 → (2a + 1) + 2 = a2
2a + 3 = a2 →
a2 - 2a - 3 = 0 → (a - 3)(a + 1) = 0
When a = 3, b = 7, and when a = -1, b = -1.
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