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

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

$Equation 1: x plus y equals 12. Equation 2: y equals x squared.$

If $the ordered pair x comma y$ is a solution to the system of equations above, which of the following is a possible value of x?

ExplanationShow

Choice D is correct. Substituting $x squared$ from the second equation for y in the first equation yields $x plus x squared, equals 12$ . Subtracting 12 from both sides of this equation and rewriting the equation results in $x squared, plus x, minus 12, equals 0$ . Factoring the left-hand side of this equation yields $open parenthesis, x minus 3, close parenthesis, times, open parenthesis, x plus 4, close parenthesis, equals 0$ . Using the zero product property to solve for x, it follows that $x minus 3, equals 0$ and $x plus 4, equals 0$ . Solving each equation for x yields $x equals 3$ and $x equals negative 4$ , respectively. Thus, two possible values of x are 3 and $negative 4$ . Of the choices given, 3 is the only possible value of x.

Choices A, B, and C are incorrect. Substituting 0 for x in the first equation gives $0 plus y, equals 12$ , or $y equals 12$ ; then, substituting 12 for y and 0 for x in the second equation gives $12 equals 0 squared$ , or $12 equals 0$ , which is false. Similarly, substituting 1 or 2 for x in the first equation yields $y equals 11$ or $y equals 10$ , respectively; then, substituting 11 or 10 for y in the second equation yields a false statement.

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

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