PSAT Math Multiple-Choice Question 630: Answer and Explanation

Question: 630

What is the value of a in this system of equations?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

(B) Since a is already solved for in the first equation, let's plug the right side of that equation into the second equation wherever there is an a:

Next, distribute the 3 and the -4:

2 + 2b + 3 = -8b - 4

You can combine the constants on the left side of the equation.

2b + 5 = -8b - 4

Now add 8b to both sides and subtract 5 from both sides:

10b = -9

Dividing by 10 gives you

However, the question asks us for the value of a. So let's plug the b-value into the first equation:

This is choice (B).

This can be solved in other ways, such as by trying elimination instead of substitution.