y = -34x + 2 3x + 4y = c In the system of equations, c is a... | SAT Systems of two linear equations in two variables Question, Answer Explained

Question bank / Systems of two linear equations in two variables

Math · AlgebraMedium

$y = -\frac{3}{4}x + 2$
$3x + 4y = c$
In the system of equations, $c$ is a constant. For what value of $c$ does the system have infinitely many solutions?

$-8$

$\frac{1}{2}$

$2$

$8$

Show answer and explanation

Answer: D

Multiply the first equation by $4$ : $4y = -3x + 8$ , which is $3x + 4y = 8$ . The system has infinitely many solutions when both equations describe the same line, so $c = 8$ .

Choice C uses the $y$ -intercept, $2$ , but the $y$ -intercept of $3x + 4y = c$ is $\frac{c}{4}$ , so $c$ must be $4 \times 2$ .

Why the other choices are wrong

A. This makes a sign error when moving the x-term. 4y = -3x + 8 becomes 3x + 4y = 8.
B. This divides 2 by 4 instead of multiplying. The y-intercept of 3x + 4y = c is c/4, which must equal 2.
C. 2 is the y-intercept of the first line. In 3x + 4y = c, the y-intercept is c/4, so c = 8.

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