Question

Solve the following pair of linear (simultaneous) equation using method of elimination by substitution:

`[3x]/2 - [5y]/3 + 2 = 0`

`x/3 + y/2 = 2 1/6`

Answer 1

`x/3 + y/2 = 2 1/6`

`x/3 + y/2 = 13/6`

⇒ `[2x + 3y]/6 = 13/6`

⇒ 2x + 3y = 13

⇒ 2x = 13 - 3y

⇒ `x = [13 - 3y]/2`                    ...(1)

And,

`[3x]/2 - [5y]/3 + 2 = 0`

⇒ `3/2([13 - 3y]/2) - [5y]/3 = - 2`

⇒ `[39 - 9y]/4 - [5y]/3 = - 2`

⇒ `[ 117 - 27y - 20y ]/12 = -2`

⇒ `[ 117 - 47y ]/12 = - 2`

⇒ 117 - 47y = - 24

⇒ 47y = 141

⇒ y = 3

Substituting the value of y in (1), we have

x = `[ 13 - 3 xx 3 ]/2`

= `[ 13 - 9 ]/2`

= `4/2`

= 2

∴ Solution is x = 2 and y = 3.