No Solution for System of Equations

Find the value of b such that the system of equations
does not have a solution.
9x - 15y = 4
bx - 10y = -19

Try 6 for b:
9x - 15y = 4------->18x - 30y = 8 {multiplied top by 2}
6x - 10y = -19---->-18x + 30y = 57 {multiplied bottom by -3}

Add the two new equations together and you get:
0 = 65, meaning there is no solution
Therefore 6 is the value of b that creates no solution


Additional note about solving with linear combinations (addition method):
- when the variables disappear and you get a statement that is never true, then there is no solution (the lines are parallel)
- when the variables disappear and you get a statement that is always true, then there are infinite solutions (the lines are the same)