SAT Nonlinear equations in one variable and systems of equations in two variables Practice Question 7 (Medium)

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

Math · Advanced MathMedium

$y = x^2$
$y = 4x - 4$
What is the solution $(x, y)$ to the system of equations above?

$(2, 4)$

$(-2, 4)$

$(4, 16)$

$(1, 1)$

Show answer and explanation

Answer: A

Set the expressions equal: $x^2 = 4x - 4$ , so $x^2 - 4x + 4 = 0$ , which factors as $(x - 2)^2 = 0$ . Thus $x = 2$ and $y = 2^2 = 4$ .

Choice B satisfies $y = x^2$ but not $y = 4x - 4$ , since $4(-2) - 4 = -12$ .

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