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Advanced Math
/ Nonlinear equations in one variable and systems of equations in two variables
Difficulty: Medium
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If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?
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Explanation
Choice A is correct. Substituting 
for y in the second equation gives 
. This equation can be solved as follows:
 | Apply the distributive property. |
 | Subtract 2x and 6 from both sides of the equation. |
 | Combine like terms. |
 | Factor both terms on the left side of the equation by 2x. |
Thus, 
and 
are the solutions to the system. Since 
, only needs to be considered. The value of y when is 
. Therefore, the value of xy is 
.
Choices B, C, and D are incorrect and likely result from a computational or conceptual error when solving this system of equations.