Solve the following system of equation by elimination method.

11x – 7y = xy, 9x – 4y = 6xy

The given equations are

11x – 7y = xy … (1)

9x – 4y = 6xy … (2)

Dividing both sides of the equation by xy,

⇒ – = 1 i.e. + = 1 … (3)

⇒ – = 6 i.e. + = 6 … (4)

Let a = and b =.

Equations (3) and (4) become

⇒ – 7a + 11b = 1 … (5)

⇒ – 4a + 9y = 6 … (6)

Now, (6) × 7 – (5) × 4

⇒ – 28a + 63b – ( – 28a + 44b) = 42 – 4

⇒ – 28a + 63b + 28a – 44b = 38

⇒ 19b = 38

⇒ b = 2

Substituting b = 2 in (5),

⇒ – 7a + 11(2) = 1

⇒ – 7a = 1 – 22 = – 21

⇒ a = 3

When a = 3, we have = 3. Thus, x =

When b = 2, we have = 2. Thus, y =

∴ (,) is the solution for the given system.