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Question if-is-

2.3 Systems Involving Nonlinear Equations - Substitution/elimination with nonlinear components
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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?

A.

0

B.

1

C.

2

D.

3

If is a solution to the system of equations above, which of the following is a

Medium-difficulty · SAT Math · Systems Involving Nonlinear Equations — Substitution/elimination with nonlinear components. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

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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