PSAT Math Multiple-Choice Question 616: Answer and Explanation

Question: 616

What are the values of x and y in the following equations?

0.75x - 0.1y = 1.2
2.6x + 3.4y = 15.4

• A. x = 1, y = -4.5
• B. x = 2, y = 3
• C. x = 3, y = 10.5
• D. x = 4, y = 18

Correct Answer: B

Explanation:

(B) Let's use elimination to get rid of the y-terms. Start by multiplying the first equation by 34: 34(0.75x - 0.1y = 1.2). This results in:

25.5x - 3.4y = 40.8

Now we can add this new equation to the second equation to eliminate the y-terms:

Dividing by 28.1 tells us that x = 2. This is enough to narrow the answer down to choice (B). However, let's solve for y just for practice:

2.6(2) + 3.4y = 15.4

5.2 + 3.4y = 15.4

Subtract 5.2 from both sides and then divide by 3.4 to learn that y = 3.