Find the value of b

Question

Find the value of b such that the system of equations

bx-20y=12

12x+16y=−11

does not have a solution. 

Answer 1

There is no solution if the lines are parallel (same slope and different y-intercepts).

For bx - 20y = 12, -20y = -bx + 12

So, y = (b/20)x - 3/5.

For 12x + 16y = -11, 16y = -12x - 11

So, y = (-3/4)x - 11/16

No solution when b/20 = -3/4

4b = -60

So, b = -15