SAT Systems of two linear equations in two variables Practice Question 12 (Medium)

Question bank / Systems of two linear equations in two variables

Math · AlgebraMedium

In the $xy$ -plane, the line $y = mx + 4$ , where $m$ is a constant, intersects the line $y = 2x - 1$ at the point where $x = 5$ . What is the value of $m$ ?

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Answer: 1

At $x = 5$ , the second line gives $y = 2(5) - 1 = 9$ . So $(5, 9)$ is on the first line: $9 = 5m + 4$ , so $m = 1$ .

Assuming the lines have the same slope gives $m = 2$ , but then they would never intersect.

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