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

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

⇒ 9x - 10y = -12         ...(i)

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

⇒ 2x + 3y = 13          ...(ii)

Taking equation (ii)

2x + 3y = 13

 ⇒ 2x = 13 – 3y

⇒ x = `(13 - 3y)/2`

Now on substituting this value of x in equation (i)

9x – 10y = -12

⇒ `9((13 - 3y)/2) - 10y = -12`

⇒ 117 – 27y – 20y = -24

⇒ 117 – 47y = -24

⇒ 47y = 117 + 24

⇒ 47y = 141

⇒ y = `141/47`

= y =  3

Now on putting y = 3 in equation (i)

⇒ x = `(13 - 3(3))/2`

= `(13 - 9)/2 = 4/2`

= x = 2

Therefore, the solution of the given pair of linear equations is

x = 2 and y = 3