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Test
Math
Domain
Advanced Math
Skill
Nonlinear equations in one variable and systems of equations in two variables
Difficulty
Medium
ID: 876a731c
Modded SAT Question Bank by Abdullah Mallik
y equals x squared
2 y plus 6, equals, 2 times, open parenthesis, x plus 3, close parenthesis

If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

  1. 1

  2. 2

  3. 3

  4. 9

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Correct Answer: A
Rationale

Choice A is correct. Substituting x squared for y in the second equation gives 2 times, x squared, plus 6, equals, 2 times, open parenthesis, x plus 3, close parenthesis. This equation can be solved as follows:

2 x squared, plus 6, equals, 2 x plus 6 Apply the distributive property.
2 x squared, plus 6, minus 2 x, minus 6, equals 0 Subtract 2x and 6 from both sides of the equation.
2 x squared, minus 2 x, equals 0 Combine like terms.
2 x times, open parenthesis, x minus 1, close parenthesis, equals 0 Factor both terms on the left side of the equation
by 2x.

Thus, x equals 0 and x equals 1 are the solutions to the system. Since x is greater than 0, only x equals 1 needs to be considered. The value of y when x equals 1 is y equals x squared, which equals 1 squared, which equals 1. Therefore, the value of xy is 1 times 1, equals 1.

Choices B, C, and D are incorrect and likely result from a computational or conceptual error when solving this system of equations.

 

Question Difficulty: Medium
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