Solve the following system of equation by elimination method.

8x – 3y = 5xy, 6x – 5y = – 2xy

The given equations are

8x – 3y = 5xy … (1)

6x – 5y = – 2xy … (2)

Dividing both sides of the equation by xy,

⇒ – = 5 i.e. + = 5 … (3)

⇒ – = – 2 i.e. + = – 2 … (4)

Let a = and b =.

Equations (3) and (4) become

⇒ – 3a + 8b = 5 … (5)

⇒ – 5a + 6y = – 2 … (6)

Now, (5) × 5 – (6) × 3

⇒ – 15a + 40b – ( – 15a + 18b) = 25 – ( – 6)

⇒ – 15a + 40b + 15a – 18b = 31

⇒ 22b = 31

⇒ b =

Substituting b = in (5),

⇒ – 3a + 8() = 5

⇒ – 3a = 5 – =

⇒ a =

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

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

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