Question

Solve for x and y : 
`[ y + 7 ]/5 = [ 2y - x ]/4 + 3x - 5`

`[ 7 - 5x ]/2 + [ 3 - 4y ]/6 = 5y - 18`

Answer 1

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.