sat suite question viewer

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

$y = 5 x + 4$ $y = 5 x + 4$

$y = 5 x^{2} + 4$ $y = 5 x^{2} + 4$

Which ordered pair $(x, y)$ $(x, y)$ is a solution to the given system of equations?

Back question 140 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 B is correct. The second equation in the given system is $y = 5 x^{2} + 4$ $y = 5 x^{2} + 4$ . Substituting $5 x^{2} + 4$ $5 x squared plus 4$ for $y$ $y$ in the first equation of the given system yields $5 x^{2} + 4 = 5 x + 4$ $5 x^{2} + 4 = 5 x + 4$ . Subtracting $4$ $4$ from both sides of this equation yields $5 x^{2} = 5 x$ $5 x squared equals 5 x$ . Subtracting $5 x$ $5 x$ from both sides of this equation yields $5 x^{2} - 5 x = 0$ $5 x^{2} - 5 x = 0$ . Factoring out a common factor of $5 x$ $5 x$ from the left-hand side of this equation yields $5 x (x - 1) = 0$ $5 x (x - 1) = 0$ . It follows that $5 x = 0$ $5 x equals 0$ or $x - 1 = 0$ $x - 1 = 0$ . Dividing both sides of the equation $5 x = 0$ $5 x equals 0$ by $5$ $5$ yields $x = 0$ $x equals 0$ . Substituting $0$ for $x$ in the equation $y = 5 x + 4$ yields $y = 5 (0) + 4$ , or $y equals 4$ . Therefore, a solution to the given system of equations is the ordered pair $left parenthesis 0 comma 4 right parenthesis$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.