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Question
Solve :
`[ 7 + x ]/5 - [ 2x - y ]/4 = 3y - 5`
`[5y - 7]/2 + [ 4x - 3 ]/6 = 18 - 5x`
Solution
`[ 7 + x ]/5 - [ 2x - y ]/4 = 3y - 5` .....(Given)
⇒ 4( 7 + x ) - 5( 2x - y ) = 20( 3y - 5 )
⇒ 28 + 4x - 10x + 5y = 60y - 100
⇒ - 6x - 55y = - 128 ......(1)
`[5y - 7]/2 + [ 4x - 3 ]/6 = 18 - 5x` ......(Given)
⇒ 3(5y - 7) + 4x - 3 = 6( 18 - 5x )
⇒ 15y - 21 + 4x - 3 = 108 - 30x
⇒ 34x + 15y = 132 .......(2)
Multiplying equation (1) by 34 and equation (2) by 6, We get
- 204x - 1870y = - 4352 .....(3)
204x + 90y = 792 ......(4)
Adding equation (3) and (4), We get
- 204x - 1870y = - 4352 .....(3)
+ 204x + 90y = 792
- 1780y = -3560
⇒ y = 2
Substituting y = 2 in equation (1), We get
- 6x - 55 x 2 = - 128
⇒ - 6x - 110 = - 128
⇒ - 6x = - 18
⇒ x = 3
∴ Solution is x = 3 and y = 2.
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