PSAT Math Multiple-Choice Question 333: Answer and Explanation

Question: 333

What is the value of x - y from the solution of the above system of equations?

• A. -5
• B. 0
• C. 2
• D. 5

Correct Answer: C

Explanation:

C

Difficulty: Medium

Getting to the Answer: Because x has a coefficient of 1 in the second equation, solve the system using substitution. Before you select your answer, make sure you found the right quantity (the difference between x and y).

First, solve the second equation for x and substitute:

Next, substitute this value back into x = 4 + 3y and simplify:

Finally, subtract x - y to find the difference:

Hence,(C) is correct. While substitution is a valid way to solve this because the second equation readily gives you x in terms of y, you could have just restated the first equation as 5x - 5y = 10 and, therefore, x - y = 2.