Question

Solve the following systems of equations:

`x/7 + y/3 = 5`

`x/2 - y/9 = 6`

Answer 1

The given system of equation is

`x/7 + y/3 = 5`  ...(i)

`x/2 - y/9 = 6`  ...(ii)

From (i), we get

`= (3x + 7y)/21 = 5`

`= 3x + 7x = 105`

`= 3x = 1.5 - 7y`

`= x = (105 - 7y)/3`

From (ii), we get

`(9x - 2y)/18 = 6`

= 9x −  2y = 108   ...(iii)'

Substituting x = `(105 - 7y)/3`  in  (iii) we get

`9(105 - 7y)/3 - 2u = 108`

`= (945 - 63y)/3 - 2y = 108`

= 945 − 63y − 6y = 108 × 3

= 945 − 69y = 324

`= 945 − 324 = 69y`

= 69y = 621

= y = 621/69 = 9

Putting y = 9 in x = `(1105 - 7y)/3` we get

`x = (105 - 7 xx 9)/3 = (105 - 63)/3`

`= x = 42/3 = 14`

Hence, the solution of thee given system of equations is x = 14, y = 9