Question

For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`[5y]/2 - x/3 = 8`

`y/2 + [5x]/3 = 12`

Answer 1

The given pair of linear equations are
`[5y]/2 - x/3 = 8`

⇒ `- x/3 + [5y]/2 = 8`               .....(1) [ On Similifying ]

`y/2 + [5x]/3 = 12`

⇒ `[5x]/3 + y/2 = 12`               .....(2) [ On Similifying ]

Multiply equation (1) by 5, we get

` -[5x]/3 + [25y]/2 = 40`         ......(3)
Adding equation (3) and (2)

          ` -[5x]/3 + [25y]/2 = 40`
    +      `[5x]/3 + y/2 = 12`       
                                                 
                        `[26y]/2 = 52`
⇒ 13y = 52
⇒ y = 4

Substituting y = 4 in equation (1), We get
`- x/3 + [5(4)]/2 = 8`
⇒ `-x/3 = 8 - 10`
⇒ x = 6
∴ Solution is x = 6 and y = 4.