PSAT Math Multiple-Choice Question 727: Answer and Explanation

Question: 727

How many solutions does the equation below have?

3x - 4y = 73

• A. None
• B. Exactly 1
• C. Exactly 2
• D. Infinite

Correct Answer: D

Explanation:

(D) Since this is one equation with two variables, it has infinite solutions. If you knew another line with which this equation intersected, the two equations would have a single solution. To see how this equation has more than two solutions, substitute some sample values for x and y into the equation:

3x - 4y = 73

If x is 1, y is -17.5.

If x is 2, y is -16.75.

If x is 3, y is -16.

You can keep on going, and you will find endless possibilities for x and y.