Solve the following pair of linear equations: 3x − 5y = 4 2y + 7 = 9x - Mathematics

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Sum

Solve the following pair of linear equations:

3x − 5y = 4
2y + 7 = 9x

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Solution

Given,

3x − 5y = 4  ...........(i)
2y + 7 = 9x  .............(ii)
From (ii), x =`(2"y" +7)/9`  ...............(iii)

substitute x = `(2"y" +7)/9` in (i), then

`3((2"y"+7)/9)-5"y" =4`

⇒ `(2"y"+7)/3 - 5"y" = 4`

⇒ `(2"y"+7-15"y")/3 = 4`

⇒ 7 - 13y = 12

⇒ `"y" = - 5/13`

Put `"y" = - 5/13` in (iii), then

`"x" = (2(-5/13)+7)/9 = (-10+91)/(9xx13)`

⇒ x = `9/13`

Hence, x = `9/13` and y=`-5/13` is the solution for the given pair of linear equations.

Concept: Pair of Linear Equations in Two Variables
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