Question

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

Answer 1

Answer:

(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.

Answer 2

Answer:

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.