PSAT Math Grid-Ins Question 98: Answer and Explanation

Question: 98

If (a, b) is a solution to the system of equations shown, what is the value of a, given that a > 0?

Correct Answer: 5

Explanation:

5

Difficulty: Hard

Category: Systems of Quadratic and Linear Equations

Getting to the Answer: Unfortunately, this is a non--calculator question, so you'll need to solve the system using substitution, rather than by graphing it on your calculator. Substitute the first equation for y into the second. Before you solve for x, multiply the whole equation by 2 to remove the fractions. Then, set the whole equation equal to 0 and factor:

Now, set each factor equal to 0 and solve to find that x = -1 and x = 5. The question asks only for a, which is the x- coordinate of the solution, so you do not need to substitute x back into an equation and solve for y. The two possible values of a are -1 and 5. Because the question specifies that a > 0, the answer must be 5. Grid in 5.