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Solution: The given system of equations is
3x + 37y = 156 (i)
-2x + 8y = 43 (ii)
Multiplying (i) by 2 and (ii) by 3, we get,
6x + 74y = 312 (iii)
-6x + 24y = 129 (iv)
Adding (iii) and (iv), we get,
98y = 441

y =

Putting this value of y in (ii), we get,
-2x + 36 = 43
-2x = 43 - 36 = 7

x

Example: Solve the following pair of equations by elimination method: 9x - 4y = 2000
and 7x - 3y = 2000.

Solution: Multiplying 9x - 4y = 2000 by 3 and 7x - 3y = 2000 by 4, we get,
27x - 12y = 6000 and 28x - 12y = 8000
Subtracting both these equations, we get,
(28x – 27x) – (12y – 12y) = 8000 – 6000
x = 2000
Substituting value of x in 9x - 4y = 2000, we get,
9(2000) – 4y = 2000
y = 4000.

Example: A number consists of two digits whose sum is 8. If 18 is added to the number,
the digits interchange their places. Represent this situation algebraically

Solution: Let the digit at ten's place be x and the digit at unit's place be y.
Then, given two digit number = 10x + y

The number after interchanging the digits = 10y + x
According to given condition,
x + y = 8 ……………….(i)
Also,10x + y + 18 = 10y + x
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