x^2 - y = 5 x + y = 7 The system of equations has two... | SAT Nonlinear equations in one variable and systems of equations in two variables Question, Answer Explained

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

Math · Advanced MathHard

$x^2 - y = 5$
$x + y = 7$
The system of equations has two solutions, $(x_1, y_1)$ and $(x_2, y_2)$ . What is the value of $y_1 + y_2$ ?

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Answer: 15

From the second equation, $y = 7 - x$ . Substitute into the first: $x^2 - (7 - x) = 5$ , so $x^2 + x - 12 = 0$ and $(x + 4)(x - 3) = 0$ . The solutions have $x = 3$ and $x = -4$ , with $y = 4$ and $y = 11$ . So $y_1 + y_2 = 4 + 11 = 15$ .

Answering $-1$ gives the sum of the $x$ -coordinates, not the $y$ -coordinates.

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