Find the relation between p and q if x = 3 and y = 1 is the solution of the pair of equations x – 4y + p = 0 and 2x + y – q – 2 = 0.

Given: x = 3 and y = 1 is the solution of the given equations:

x – 4y + p = 0

and 2x + y – q – 2 = 0

To find: Relation between p and q

Proof:

On taking

⇒ -q – 2 = 2p

⇒ 2p + q + 2 = 0

It is given that x = 3 and y = 1 is the solution of the equation

x – 4y + p = 0 …(i)

and 2x + y – q – 2 = 0 …(ii)

Substituting the value x = 3 and y = 1 in eq.(i), we get

(3) – 4(1) + p = 0

⇒ 3 – 4 + p = 0

⇒ -1 + p = 0

⇒ p = 1

So, eq. (i) become

x – 4y + 1 = 0

Substituting the value x = 3 and y = 1 in eq.(ii), we get

2(3) + (1) – q – 2 = 0

⇒ 6 + 1 – q – 2 = 0

⇒ -q + 5 = 0

⇒ q = 5

So, eq. (ii) become

2x + y – 5 – 2 = 0

or 2x + y – 7 = 0