Question

For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
`[ x - y ]/6 = 2( 4 - x )`
2x + y = 3( x - 4 )

Answer 1

The given pair of linear equations are
`[ x - y ]/6 = 2( 4 - x )`

⇒ x - y = 12(4 - x)
⇒ x - y = 48 - 12x
⇒ 13x - y = 48                      ....(1) [ On simplifying ]

2x + y = 3( x - 4 )
⇒ 2x + y = 3x - 12
⇒ x - y = 12                         .....(2) [ On simplifying ]

Multiply equation (2) by 13, We get,
13x - 13y = 156                   .....(3)

Subtracting equation (1) from (3)
            13x - 13y = 156 
       -    13x -   y   =  48  
            -      +         -       
                    - 12y = 108
                         y = - 9
Substituting y = - 9 in equation (1), we get
13x - ( - 9) = 48
⇒ 13x = 39
⇒ x = 3
∴ Solution is x = 3 and y = - 9.