# Solve the followi

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.

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