sat suite question viewer

Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Easy

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

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?

Back question 54 of 148 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

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.