Question

Which values of m and b will create a system of equations with no solution? Select two options.

y = mx + b

y = –2x + A system of equations. y equals m x plus b. y equals negative 2 x plus StartFraction 3 over 2 EndFraction.

A coordinate grid with a line labeled y equals negative 2 x plus StartFraction 3 over 2 EndFraction and passes through the points (9, 1.5) and (1, 0.5).

m = –3 and b = negative StartFraction 2 over 3 EndFraction.
m = –2 and b = m equals negative 3 and b equals negative StartFraction 1 over 3 EndFraction.
m = 2 and b = negative StartFraction 2 over 3 EndFraction.
m = m equals StartFraction 3 over 2 EndFraction and b equals negative StartFraction 2 over 3 EndFraction and b = m equals negative StartFraction 3 over 2 EndFraction and b equals negative StartFraction 2 over 3 EndFraction
m = -2 and b = m equals negative 2 and b equals negative StartFraction 2 over 3 EndFraction

Answer 1

No solution occurs when the two lines are parallel but not identical — so m must equal -2 and b must not equal 3/2.

The two choices with m = -2 and b ≠ 3/2 are:
- m = -2, b = -1/3
- m = -2, b = -2/3

(both have slope -2 and intercepts different from 3/2, so the lines are distinct and parallel.)