SAT Systems of two linear equations in two variables Practice Question 17 (Hard)

Question bank / Systems of two linear equations in two variables

Math · AlgebraHard

In the $xy$ -plane, the lines $y = 4x - 9$ and $y = -2x + c$ , where $c$ is a constant, intersect at the point $(h, k)$ . If $k = 2h$ , what is the value of $c$ ?

$0$

$9$

$13.5$

$18$

Show answer and explanation

Answer: D

The point $(h, 2h)$ is on the first line, so $2h = 4h - 9$ , giving $h = 4.5$ and $k = 9$ . The point $(4.5, 9)$ is also on the second line: $9 = -2(4.5) + c = -9 + c$ , so $c = 18$ .

Choice B is the value of $k$ , the $y$ -coordinate of the intersection point, not $c$ .

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