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)
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