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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