y = 2x^2 - 3x + c y = 5x + 1 In the system of equations, c is... | 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

$y = 2x^2 - 3x + c$
$y = 5x + 1$
In the system of equations, $c$ is a constant. For what value of $c$ does the system have exactly one distinct real solution?

$7$

$8$

$9$

$17$

Show answer and explanation

Answer: C

Set the expressions equal: $2x^2 - 3x + c = 5x + 1$ , so $2x^2 - 8x + (c - 1) = 0$ . The system has exactly one solution when this quadratic has exactly one real solution, which happens when its discriminant is $0$ : $(-8)^2 - 4(2)(c - 1) = 0$ . Then $64 = 8(c - 1)$ , so $c - 1 = 8$ and $c = 9$ .

Choice B stops at $c - 1 = 8$ and forgets to add $1$ .

Why the other choices are wrong

A. This subtracts 1 from 8 instead of adding it. Since c - 1 = 8, c = 9.
B. 8 is the value of c - 1, not c.
D. This uses 4 instead of 4 × 2 in the discriminant, which leaves out the leading coefficient, 2.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free, or take a free full-length practice test.