PSAT Math Multiple-Choice Question 341: Answer and Explanation

Question: 341

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

• A. -9
• B.
• C.
• D. 9

Correct Answer: B

Explanation:

B

Difficulty: Hard

Getting to the Answer: A system of equations that has infinitely many solutions describes a single line. Therefore, manipulation of one equation will yield the other. Look at the constant terms: to turn the 24 into -2, divide the first equation by -12:

The y term and the constant in the first equation now match those in the second. All that's left is to set the coefficients of x equal to each other: . Choice (B) is correct.

Note that you could also write each equation in slope--intercept form and set the slopes equal to each other to solve for q.