The given equations are 6x + 3y = 7xy and 3x + 9y = 11xy.

Dividing by xy on both sides of the given equations, we get

Then,

… (1)

… (2)

If we substitute and in (1) and (2), we get

3p + 6q = 7 … (3)

9p + 3q = 11 … (4)

Now by elimination method,

Step 1: Multiply equation (3) by 3 and equation (4) by 1 to make the coefficients of x equal.

Then, we get the equations as:

9p + 18q = 21 … (5)

9p + 3q = 11 … (6)

Step 2: Subtract equation (6) from equation (5),

(9p – 9p) + (3q – 18q) = 11 – 21

⇒ - 15q = - 10

⇒

Step 3: Substitute q value in (3),

3p = 3

⇒ p = 1

We know that and .

Substituting values of p and q, we get

x = 1 and y =

The solution is x = 1 and y = .