For what value of p and q the following system has infinite number of solutions?

2x + 3y = 7

(p–q) x + (2p+q) y = 21

Given: The system of equations:

2x + 3y = 7

(p–q) x + (2p+q) y = 21

To find:

The value of p and q.

Explanation:

If …… (1)

Then system of equations has infinite number of solutions.

Here,

a₁= 2 a₂ = (p–q)

b₁= 3 b₂ = (2p+q)

c₁= 7 c₂ = 21

For given values:

From (1),

⇒ p – q = 6 …. (1)

q = p + 6

2p + q = 9 …. (2)

Put the value of q in (2) to get,

⇒ 2p+p+6=9

⇒ 3p+6=9

⇒ 3p=3

⇒ p = 1

Put this value in (1) we get,

q = 1 + 6

= 7

Hence the values of p and q are 1 and 7.