Question

Solve the following pairs of linear (simultaneous) equation using method of elimination by substitution:
`x/6 + y/15 = 4`

`x/3 - y/12 = 4 3/4` 

Answer 1

`x/6 + y/15 = 4`     

⇒ `[ 5x + 2y ]/30 = 4`

⇒ 5x + 2y = 120
⇒ 5x = 120 - 2y

⇒ x = `[ 120 - 2y ]/5`                   ....(1)

And,
`x/3 - y/12 = 4 3/4`

⇒ `1/3( x - y/4 ) = 19/4`

⇒ `1/3([120 - 2y]/5 - y/4 ) = 19/4`

⇒ `[ 480 - 8y - 5y ]/20 = 57/4` 

⇒ `[ 480 - 13y ]/20 = 57/4`

⇒ 480 - 13y = 285
⇒ 13y = 195
⇒ y = 15
Substituting the value of y in (1), we have

`x = [ 120 - 2 xx 15]/5 = [120 - 30]/5 = 90/5 = 18`
∴ Solution is x = 18 and y = 15