y = x^2 - 2x - 3 y = x + 1 If (a, b) is a solution to the... | 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 MathMedium

$y = x^2 - 2x - 3$
$y = x + 1$
If $(a, b)$ is a solution to the system of equations and $a > 0$ , what is the value of $b$ ?

$0$

$1$

$4$

$5$

Show answer and explanation

Answer: D

Set the expressions for $y$ equal: $x^2 - 2x - 3 = x + 1$ , so $x^2 - 3x - 4 = 0$ and $(x - 4)(x + 1) = 0$ . The positive solution is $x = 4$ , so $a = 4$ and $b = 4 + 1 = 5$ .

Choice C is the value of $a$ , not $b$ .

Why the other choices are wrong

A. 0 is the y-coordinate of the other solution, (-1, 0), where a is negative.
B. 1 is the y-intercept of the line y = x + 1, not a y-coordinate of an intersection point.
C. 4 is the x-coordinate, a. The y-coordinate is b = 4 + 1 = 5.

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