Question

`x/3 + y/2 = 4, x/2 + y/4 = 4`

Answer 1

Here,

`x/3 + y/2 = 4`    ...(1)

`x/2 + y/4 = 4`    ...(2)

Multiply equation (1) by 6:

`6(x/3) + 6(y/2) = 6(4)`

2x + 3y = 24    ...(3)

Multiply equation (2) by 4:

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

2x + y = 16    ...(4)

Now, subtracting equation (4) from equation (3):

(2x + 3y) − (2x + y) = 24 − 16

2x + 3y − 2x − y = 8

2y = 8

y = `8/2`

∴ y = 4

Substituting y = 4 in equation (4):

2x + 4 = 16

2x = 16 − 4

2x = 12

x = `12/2`

∴ x = 6