Q25 of 186 Page 3

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

4x + py + 8 = 0, 2x + 2y + 2 = 0

Given, pair of equations


4x + py + 8 = 0


and 2x + 2y + 2 = 0


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


a1 = 4, b1 = p and c1 = 8


and a2 = 2, b2 = 2 and c2 = 2


For unique solutions,



Here,


∴


On taking I and II terms, we get



⇒ p≠4


Thus, given lines have a unique solution for all real values of p, except 4.


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