SAT Exam > SAT Questions > y = x22y + 6 = 2(x + 3)If (x, y) is a solutio...
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y = x2
2y + 6 = 2(x + 3)
If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy?
2y + 6 = 2(x + 3)
If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy?
- a)1
- b)2
- c)3
- d)9
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
y = x22y + 6 = 2(x + 3)If (x, y) is a solution of the system of equati...
Substituting x2 for y in the second equation gives 2(x2) + 6 = 2(x + 3). This equation can be solved as follows:
2x2 + 6 = 2x + 6 (Apply the distributive property.)
2x2 + 6 − 2x − 6 = 0 (Subtract 2x and 6 from both sides of the equation.)
2x2 − 2x = 0 (Combine like terms.)
2x(x − 1) = 0 (Factor both terms on the left side of the equation by 2x.)
Thus, x = 0 and x = 1 are the solutions to the system. Since x > 0, only x = 1 needs to be considered. The value of y when x = 1 is y = x2 = 12 = 1. Therefore, the value of xy is (1)(1) = 1. Choices B, C, and D are incorrect and likely result from a computational or conceptual error when solving this system of equations.
2x2 + 6 = 2x + 6 (Apply the distributive property.)
2x2 + 6 − 2x − 6 = 0 (Subtract 2x and 6 from both sides of the equation.)
2x2 − 2x = 0 (Combine like terms.)
2x(x − 1) = 0 (Factor both terms on the left side of the equation by 2x.)
Thus, x = 0 and x = 1 are the solutions to the system. Since x > 0, only x = 1 needs to be considered. The value of y when x = 1 is y = x2 = 12 = 1. Therefore, the value of xy is (1)(1) = 1. Choices B, C, and D are incorrect and likely result from a computational or conceptual error when solving this system of equations.
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