PSAT Math Multiple-Choice Question 331: Answer and Explanation

Question: 331

In the system of linear equations shown, z represents a constant. If the system of equations has infinitely many solutions, what is the value of z ?

• A.
• B. 5
• C. 8
• D. 40

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Number of Possible Solutions

Getting to the Answer: A system of equations that has infinitely many solutions results when you can algebraically manipulate one equation to arrive at the other. Examining the right sides of the equations, you see that 40 × 40 = 1,600; therefore, multiplying the first -equation by 40 will give 1,600 on the right: 5q + 8s = 1,600. The first equation is now identical to the second equation, meaning z must be 5, which is (B).