Find the value of b such that the system of equations does not have a solution.

Question

-10x + 4y = 1

-15x + by = -6

Answer 1

If they are parallel (slope is the same) and not identical lines then no solution.

-10x + 4y = 1

4y = 1 + 10x

y = 1/4 + 10/4 x, slope 10/4

-15x + by = -6

by = -6 + 15x

y = -6/b +15/b x

So we need 15/b = 10/4

and 1/4 <> -6/b (otherwise lines are the same)

15/b = 10/4.

10b = 60

b = 6

-6/b = -1 <> 1/4 as required

so b=6