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Sum

Solve the following simultaneous equations.

`x/3 + y/4 = 4; x/2 - y/4 = 1`

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#### Solution

`x/3 + y/4 = 4` .....(I)

`x/2 - y/4 = 1` ......(II)

Multiplying (I) with LCM of 3 and 4 which is 12, we get

`4x + 3y = 48` .......(III)

Multiplying (II) with LCM of 2 and 4 which is 4, we get

2x - y = 4 .......(IV)

Multiplying (IV) with 2

4x - 2y = 8 .......(V)

Subtracting (V) from (III)

5y = 40

⇒ y = 8

Putting this value of y in (IV) we get

2x - 8 = 4

⇒ 2x = 12

⇒ x = 6.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method

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