Question

Find the values of $p$ and $q$ if the pair of equations have infinitely many solutions.

$2x+3y=7$ and $2px+py=28-qy$

Answer 1

Given equations are
$2x+3y=7$ ...(i)
$2px+py=28-qy\Rightarrow \frac{p}{2}x+\frac{p+q}{4}y=7$ ...(ii)
For the pair of equations have infinitely many solutions coefficient of x and y should be same.
On comparing (i) and (ii), we get
$\frac{p}{2}=2$ and $\frac{p+q}{4}=3$
$\Rightarrow p=4$
and $p+q=12\Rightarrow q=12-p=12-4=8$
Hence, $p=4,q=8$