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?

Answer 1

m = -3, b = 5

Explanation:

The values m = -3 and b = 5, forms a linear equation: y = -3x + 5. This obviously coincides with the original equation given, and so will create a system of linear equations with no solution.

Answer 2

m = - 3 and b = - 3.

Explanation:

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

Two equations are parallel:

1. if their slopes (m) are equal

2. the y-intercep (b) are different.

As 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.