SAT Nonlinear equations in one variable and systems of equations in two variables Practice Question 11 (Medium)

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Question bank / Nonlinear equations in one variable and systems of equations in two variables

Math · Advanced MathMedium

$y = x^2 - 3$
$y = 2x$
Which of the following is a solution $(x, y)$ to the system of equations above?

$(1, 2)$

$(-3, -6)$

$(-1, 2)$

$(3, 6)$

Show answer and explanation

Answer: D

Substitute: $x^2 - 3 = 2x$ , so $x^2 - 2x - 3 = 0$ and $(x - 3)(x + 1) = 0$ . If $x = 3$ , $y = 6$ ; if $x = -1$ , $y = -2$ . Of the choices, only $(3, 6)$ is a solution.

Choice C has the correct $x$ -value $-1$ but the wrong sign for $y$ ; $y = 2(-1) = -2$ .

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