PSAT Math Multiple-Choice Question 177: Answer and Explanation

Question: 177

If (x, y) represents the solution to the system of equations shown above, what is the value of y ?

• A. 10
• B. 19
• C. 29
• D. 31

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Heart of Algebra/Systems of Linear Equations

Getting to the Answer: When a system consists of two equations already written in terms of y, the quickest way to solve the system is to set the equations equal to each other and then use inverse operations. Don't let the fraction intimidate you—you can write the first equation as a fraction over 1 and use cross--multiplication:

Don't let (A) fool you—the question is asking for the value of y, not the value of x. To find y, substitute 10 for x in either equation and simplify:

Choice (C) is correct.