y 3x - 7 y < -x + 9 The point (3, b) is a solution to the... | SAT Linear inequalities in one or two variables Question, Answer Explained

Question bank / Linear inequalities in one or two variables

Math · AlgebraMedium

$y > 3x - 7$
$y < -x + 9$
The point $(3, b)$ is a solution to the system of inequalities. How many integer values of $b$ are possible?

Student-produced response: enter your answer.

Show answer and explanation

Answer: 3

Substitute $x = 3$ . The first inequality gives $b > 3(3) - 7 = 2$ , and the second gives $b < -3 + 9 = 6$ . So $2 < b < 6$ , and the integers in this range are $3$ , $4$ , and $5$ . There are $3$ possible values.

Counting the boundary values $2$ and $6$ gives $5$ , but both inequalities are strict.

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.