PSAT Math Multiple-Choice Question 105: Answer and Explanation

Question: 105

-4j - 10k = 50

j - 3k = 4

If (j, k) is the solution to the system of equations above, what is the value of j?

• A. 13
• B. -5
• C. -7
• D. -10

Correct Answer: B

Explanation:

B

The question asks for the value that satisfies a system of equations. There are specific values in the answers, so plug in the answers. The answer choices represent possible values of j. Test the values in both equations from the question and look for one that makes both equations the same. Start with (B). Plug the value into the first equation to get (-4)(-5) - 10k = 50. This becomes 20 - 10k = 50. Subtract 20 from both sides to get -10k = 30 or k = -3. Then plug the value into the second equation to get (-5) -3k = 4. Add 5 to both sides to get -3k = 9 or k = -3. This is the same as the first equation with this value. The correct answer is (B).