41. The equations below are linear equations of a system where a, b, and c are positive integers.

ay + bx = c

ay - bx = c

Which of the following describes the graph of at least 1 such system of equations in the standard (x, y) coordinate plane?

I. 2 parallel lines

II. 2 intersecting lines

III. A single line

Answer and Explanation

Your Answer is

Correct Answer is B

Explanation

The slopes of two linear equations must be equal for the two lines to be parallel. Because the title requires b to be a positive number, and the signs of b in the two equations are opposite, the two lines cannot be parallel, and I is excluded. For two lines to be one, they must be completely coincident, that is, have equal coefficient ratios. Likewise, the opposite sign of b rules out this possibility. So the two lines must intersect. So choose B.