Question

Solve the following systems of equations:

`x + y/2 = 4`

`x/3 + 2y = 5`

Answer 1

The given system of equation is

`x + y/2 = 4` .......(i)

`x/3 + 2y = 5` ....(ii)

From (i), we get

`(2x + y)/2 = 4`

2x + y = 8

y = 8 - 2x

From (ii), we get

x + 6y = 15 ....(iii)

Substituting y = 8 - 2x in (iii), we get

x + 6(8 - 2x) = 15

`=> x + 48 - 12x = 15`

=> -11x = 15 - 48

=> -11x = -33

`=> x = (-33)/(-11) = 3`

Putting x = 3 in y = 8 - 2x we get

y = 8 - 2 x 3

= 8 - 6

= 2

y = 2

Hence, solution of the given system of equation is x= 3, y = 2