Written in the form y = mx + b, the two rules in a system share the sa…

Question

Written in the form y = mx + b, the two rules in a system share the same value of m but have different values of b. What follows?

Accepted Answer

C. The lines are parallel, so there is no solution

1. The value of m is the slope, so equal values of m mean the two lines lean at the same angle.
2. The value of b is where each line meets the upright axis, so different values place the lines at different heights.
3. Two lines that lean the same way but sit at different heights stay the same distance apart forever.
4. Lines like that never meet, so no pair of values satisfies both rules.
5. Option B would need the values of b to match as well, which is exactly what is ruled out here.
6. Option A would need different values of m, since only different slopes force a crossing.
7. Option D fails because two straight lines can never meet more than once.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_

Answer

The lines cross once, so there is one solution

Answer

The lines are the same, so every point fits

Answer

The lines cross twice, so there are two answers