SAT Nonlinear equations in one variable and systems of equations in two variables Practice Question 20 (Hard)

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

Math · Advanced MathHard

$x^2 + y^2 = 25$
$y = x + 1$
The system of equations above has two solutions. If $(a, b)$ is the solution with $a < 0$ , what is the value of $ab$ ?

$-12$

$7$

$12$

$25$

Show answer and explanation

Answer: C

Substitute $y = x + 1$ : $x^2 + (x + 1)^2 = 25$ , so $2x^2 + 2x - 24 = 0$ and $x^2 + x - 12 = 0$ . Factoring gives $(x + 4)(x - 3) = 0$ . The solution with $a < 0$ has $a = -4$ and $b = -3$ , so $ab = 12$ .

Choice A comes from using $b = 3$ , forgetting that $b = a + 1 = -3$ .

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