PSAT Math Multiple-Choice Question 342: Answer and Explanation

Question: 342

In the system of linear equations shown above, z is a constant. If the system has no solution, what is the value of z ?

• A.
• B.
• C. 8
• D. 10

Correct Answer: A

Explanation:

A

Difficulty: Hard

Getting to the Answer: A system of linear equations that has no solution should describe two parallel lines. This means the coefficients of the variables should be the same (so the slopes of the lines are the same). Only the constant should be different (so the y-intercepts are not the same). The easiest way to make the coefficients the same is to manipulate the second equation. Multiplying the second equation by 40 would make the coefficients of x the same in both equations: 8x + 40 zy = 20. Now, equate the coefficients of y to get 4y = 40 zy. Solve for z to reveal that , which is (A). Alternatively, you could write each equation in slope-intercept form and set the slopes equal to each other to solve for z.