Question

1. a system of two linear equations has one solution. what must b

a) they are parallel.
b) they are perpendicular.
c) they are the same line.
d) they intersect.

Explanation:

To determine the correct option, we analyze each choice based on the properties of linear equations:

• Option A: Parallel lines have the same slope and never intersect, so they have no solution. Eliminate A.
• Option B: Perpendicular lines have slopes that are negative reciprocals, but this only describes their slope relationship, not the number of solutions. Two perpendicular lines (that are not the same) intersect at one point, but the key here is the condition for one solution. However, the defining condition for one solution is intersection (not just perpendicularity). Eliminate B.
• Option C: If two lines are the same, they are coincident and have infinitely many solutions (all points on the line). Eliminate C.
• Option D: For a system of two linear equations, the solution is the point where the lines intersect. If there is one solution, the lines must intersect at exactly one point. This matches the condition for one solution.

Answer:

D. They intersect.