Question

For what value of p will the following pair of linear equations have infinitely many solutions.
$\left(p-3\right)x+3y=p$
$px+py=12$

Answer 1

Consider the given equations.

$(p-3)x+3y=p$

$px+py=12$

Since, this pair of linear equations have infinite many solution.

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Therefore,

$\frac{p-3}{p}=\frac{3}{p}=\frac{p}{12}$

Om solving equations, we get

$p=6$

Hence, this is the answer.