Q. 124.6( 5 Votes )

For what value of

Answer :

given pair of linear equations are


(p – 3) x + 3y = p


(p – 3) x + 3y – p = 0


px + py = 12


px + py – 12 = 0


Comparing these with standard equation


a1x1 + b1x1 + c1 = 0 and a2x2 + b2x2 + c2 = 0


We get


a1 = (p – 3), b1 = 3, c1 = – p


a2 = p, b2 = p, c2 = – 12


Now it is given the linear pair of equations have infinitely many solutions, so the condition for it is:



Now substituting the corresponding values, we get



Considering first equality, we get



p – 3 = 3


p = 6


Considering the second equality, we get




3 × 12 = p2


p = √36


p = ±6


Hence p = + 6 satisfies both the conditions.


Hence for p = 6, the given pair of linear equations have infinitely many solutions.

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