Question

which term describes the scenario when two linear equations have the same slope but different y-intercepts?
a. intersecting
b. coincident
c. parallel
d. perpendicular

which scenario represents a system of equations with no solution?
a. two parallel lines that never intersect
b. two lines that are identical
c. two lines intersecting at one point
d. two perpendicular lines

Explanation:

Step1: Identify line property

For linear equations $y=mx+b$, same $m$ (slope), different $b$ (y-intercept) means lines never cross, so they are parallel.

Step2: Analyze no-solution systems

A system has no solution if lines do not intersect. Parallel non-coincident lines never intersect, so this is the scenario. Identical lines have infinite solutions; intersecting/perpendicular lines have one solution.

Answer:

1. c. Parallel
2. a. Two parallel lines that never intersect