Question

Consider this system of linear equations:

y = –3x + 5

y = mx + b

Which values of m and b will create a system of linear equations with no solution?

m = –3 and b = –3
m = 5 and b = –3
m = 3 and b = 5
m = 5 and b = –3

Engenuity answer is m= -3 and B= -3

Answer 1

m = –3 and b = –3 or A

Answer 2

Answer: m = - 3 and b = - 3.

Justification:

A system of linear equations will not have solutions if the two lines are parallel.

Two equations are parallel if their slopes (m) are equal and the y-intercep (b) are different.

Since the given equation is y = - 3x + 5, the value of m of the other equation, y = mx + b, in order to make a system with no solution, needs to be - 3, and the value of b need to be different to 5.

The only pair from the choices that meets that is the first option m = - 3 and b = -3.