Question

by inspection, which system would have no solution?
○ line a and line b
○ line a and line c
○ line b and line c
○ line b and line d

Explanation:

Step1: Recall no solution condition

A system of linear equations has no solution if the lines are parallel (same slope) and distinct (different y-intercepts, never intersect).

Step2: Analyze line slopes

• Line b (red) and line c (blue) are both downward-sloping, parallel (same slope), and never intersect.
• Line a intersects b, c, d; line b intersects d; line a intersects c.

Answer:

line b and line c