Question

Solve the following pair of linear equations by the substitution method.

`(3x)/2 - (5y)/3 = -2`

`x/y+y/2 = 13/6`

Answer 1

`3/2x - 5/3y = -2 ....(1)`

`x/3+y/2=13/6.....(2)`

From equation (1), we obtain

9x - 10y = -12

`x = (-12+10y)/9 `

Substituting this value in equation  (2), we obtain

`((-12+10y)/9)/3 + y/2 = 13/6`

`(-12+10y)/27+y/2 = 13/6`

`(-24+20y+27y)/54 = 13/6`

47y = 117 + 24

47y = 141

y = 3   (4)

Substituting this value in equation (3), we obtain

x = `(-12+10xx3)/9 = 18/9 = 2`

Hence, x = 2, y = 3