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Solve Linear Equation in Two Variables
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4. Addition-Substration Method
Solve linear equations 7Y+2X-11=0 and 3X-Y-5=0 using Addition-Substriaction Method

`2X+7Y-11 = 0 ->(i)`

`3X-Y-5 = 0 ->(ii)`

Adding Equation `(i)` and `(ii)`, we get

`5X+6Y-16 = 0`

`5X+6Y-16 = 0 ->(iii)` (On simplifying)

Subtracting Equation `(ii)` from `(i)`, we get

`-X+8Y-6 = 0`

`X-8Y+6 = 0 ->(iv)` (On simplifying)

`5X+6Y = 16 ->(1)`

`X-8Y = -6 ->(2)`

Eqn.`(1) xx 1 => 5X+6Y = 16`

Eqn.`(2) xx 5 => 5X-40Y = -30`

Substracting `=> 46Y = 46`

`=> Y = 46 / 46`

`=> Y = 1`

Putting `Y = 1` in Eqn. `(2)`, we have

`X-8(1) = -6`

`=> X = -6+8`

`=> X = 2`

`=> X = 2`

`:. X = 2" and "Y = 1`

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