Q25 of 186 Page 3

Find the value of a for which the following system of equations has unique solution:

3x + 2y = 4, ax – y = 3

Given, pair of equations


3x + 2y = 4


and ax – y = 3


On comparing the given equation with standard form i.e. a1 x + b1y + c1 = 0 and a2 x + b2y + c2 = 0, we get


a1 = 3, b1 = – 2 and c1 = – 4


and a2 = a, b2 = – 1 and c2 = – 3


For unique solutions,



Here,


∴


On taking I and II terms, we get




Thus, given lines have a unique solution for all real values of a, except .


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