Question

Solve by reducing them to a pair of linear equations. 1/2x + 1/3y =2 and 1/3x + 1/2y = 13/6​

Answer 1

Answer:

the value of x=2 and y=3

Answer 2

Answer:

let 1/x = a and 1/y= b

1/2x + 1/3y =2

a/2 + b/3 = 2

3a + 2b = 12 .....…......(1)

1/3x +1/2y =13/6

a/3 + b/ 2 = 13/6

2a +3b = 13 ........…......(2)

from equation (1 ) we have,

a = (12-2b)/3 ...….......(3)

substituting the value of a in equation (2)

2(12-2b)/3 + 3b =13

24 - 4b +9b = 39

5b = 39-24 =15

b = 15/5 = 3

b=3

from equation (3),

a = (12- 2× 3 )/3

a = 6/3 = 2

a=2

1/x = a => 1/a = x

x = 1/2

1/y = b => 1/b = y

y = 1/3