Question

Solve the following simultaneous equation.

`1/3x + y = 10/3` ; `2x + 1/4y = 11/4`

Answer 1

`1/3x + y = 10/3`           ...(I)

`2x + 1/4y = 11/4`        ...(II)

Multiply (I) with 3 and (II) with 4

x + 3y = 10       ...(III)

8x + y = 11      ...( IV)

Multiply (IV) with 3

24x + 3y = 33         ...(V)

Subtracting (V) from (III)

⇒ x - 24x + 3y - 3y = 10 - 33

⇒ -23x = -23

⇒ x = 1

Putting the value of x = 1 in (III)

1 + 3y = 10

3y = 10 - 1

3y = 9

y = `9/3`

y = 3

Thus, (x, y) = (1, 3)