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 = - 3 and b = 5

(A) m = - 3 and b = - 3

Step-by-step explanation:

If m=-3 and b=-3

The system of linear equations:

y = - 3x + 5

y = mx + b

Becomes

y = - 3x + 5 ... (i)

y = - 3x - 3 ... (ii)

Notice that 5 is added to - 3x in (i) and - 3 is added to - 3x in (ii) and both equals y. This is impossible. Thus the system has no solution.

m = - 3 and b = - 3

Step-by-step explanation:

y = - 3x + 5 (1)

A system has no solution when we have an inconsistency. The case where an inconsistency remains is when m = - 3 and b = - 5. In the following way:

y = - 3x - 3 (2)

if I multiply by - 1 (2) and the add to (1). We have left

y = - 3x + 5

-y = 3x + 3

0 = 0 + 8

And 0 is not equal to 8, therefore it is inconsistent.