AlgebraMediumSolution of a system by elimination
Algebra practice question
Which ordered pair (x, y) satisfies the system 2x + 3y = 14 and x − y = 2?
- A. (4, 2)Correct
- B. (2, 4)
- C. (5, 3)
- D. (1, 4)
Answer: A. (4, 2)
From the second, x = y + 2. Substitute: 2(y + 2) + 3y = 14, so 5y = 10, y = 2, x = 4.
Why the other answers are wrong
- B. (2, 4)
- (2, 4): 2 − 4 = −2, not 2.
- C. (5, 3)
- (5, 3): 10 + 9 = 19, not 14.
- D. (1, 4)
- (1, 4): 2 + 12 = 14 ✓, but 1 − 4 = −3.
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