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Example : Solve the given system of equations:
101x + 99y = 499
99x + 101y = 501

Solution: Given system of equations:
101x + 99y = 499 ……. (1)
99x + 101y = 501 ………(2)

Adding (1) and (2), we get,

200 x + 200 y = 1000
or x + y = 5 (dividing by 200) ….(3)
Subtracting (2) from (1), we get,

2 x - 2 y = -2
or x - y = -1 (dividing by 2) …. (4)

Adding these equations, we get,
2 x = 4 or x = 2.
Thus, y = 3 from eq (3)

The required solution is x = 2 and y = 3.

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