system

For this set of linear equations to have no solitution, the slopes must be the same so they are parallel lines.

First, rearange the equations so they are in y= form.

15x-18y=-19

subtract 15x

-18y=-19-15x

divide by -18

y=19/18 + 5/6x

The slope of this line is 5/6.

bx-12y=12

subtract bx

-12y=12-bx

divide by -12

y=(b/12)x-1

The slope is b/12.

 

For no solitution the slopes are the same so

5/6=b/12

multiply by 12

10=b