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Nonlinear equations in one variable and systems of equations in two variables SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

$y equals x squared$

$2 y plus 6, equals, 2 times, open parenthesis, x plus 3, close parenthesis$

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

ExplanationShow

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.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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