Q. 124.3( 9 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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