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

Question

12x+20y=-7

bx-15y=-5

Answer 1

There is more than one way to work this. The easiest may be to write both equations in slope-intercept form, and then choose the value for b that makes the lines parallel, but with different y-intercepts.

Slope of first line:

m = -12/20 = -3/5

Make the slope of the second line equal to -3/5.

-3/5 = -b/-15 = b/15

b = -9

You can also set the principal determinant equal to zero, and solve for b.

D = 12(-15) - 20b = 0

20b = -180

b = -9