Find the values of `p` and `q` for which the following system of equations has infinite number of solutions: `2x+3y=7,\ \ \ \ (p+q)x+(2p-q)y=21`

Explanation

The given system of equations is
2x + 3y = 7
(p + q)x + (2p - q)y = 21
Here `a_(1) = 2, b_(1) = 3`, and `c_(1) = 7`
`a_(2) = p + q, b_(2) = 2p - q` and `c_(2) = 21`
The given system will have infinite number of solutions if
`(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))`
`(2)/(p + q) = (3)/(2p - q) = (7)/(21)`
Taking first two and last two expressions
`(7)/(p + q) = (1)/(3)` and `(3)/(2p - q) = (1)/(3)`
implies p + q = 6 and 2p - q = 9
Solving p + q = 6 and 2p - q = 9, we get
p = 5 and q = 1
Hence, the given system of equations will have infinitely many solutions, if p = 5 and q = 1.