PSAT Math Multiple-Choice Question 344: Answer and Explanation

Question: 344

If the system of linear equations shown above has infinitely many solutions, and c is a constant, what is the value of c ?

• A.
• B.
• C. 2
• D. 12

Correct Answer: B

Explanation:

B

Difficulty: Hard

Getting to the Answer: A system of linear equations has infinitely many solutions if both lines in the system have the same slope and the same y-intercept (in other words, they are the same line). Write each of the equations in slope-intercept form, y = mx + b. Their slopes should be the same. To find c, set the y-intercepts, b, equal to each other and solve. Before rewriting the equations, multiply the first equation by 6 to make it easier to manipulate.

First equation:

Second equation:

Set the y-intercepts equal:

Hence, (B) is correct.