PSAT Math Multiple-Choice Question 192: Answer and Explanation

Question: 192

If the system of linear equations above has no solution, and a is a constant, what is the value of a ?

• A.
• B.
• C.
• D. 3

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Heart of Algebra/Systems of Linear Equations

Getting to the Answer: Graphically, a system of linear equations that has no solution indicates two parallel lines, or in other words, two lines that have the same slope. So, write each of the equations in slope-intercept form (y = mx + b) and set their slopes (m) equal to each other to solve for a. Before finding the slopes, multiply the top equation by 3 to make it easier to manipulate:

The slope of the first line is and the slope of the second line is . Now, set the slopes equal to each other and solve:

Choice (D) is correct.