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Question
Solve for x and y :
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
Solution
The given pair of linear equation are
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`
⇒ 55x + 6y = 128 ....(1)[ On simplifying ]
`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`
⇒ 15x + 34y = 132 ....(2)[ On simplifying ]
Multiply equation (1) by 3 and equation (2) by 11, we get :
165x + 18y = 384 ....(3)
165x + 374y = 1452 .....(4)
Subtracting (4) from (3)
165x + 18y = 384
- 165x + 374y = 1452
- - -
- 356y = - 1068
y = 3
Substituting y = 3 in equation (1), we get
55x + 6(3) = 128
⇒ 55x = 110
⇒ x = 2
∴ Solution is x = 2 and y = 3.
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