Question

solve the following pair of equation by reducing them to pair of linear equation.
1/2x + 1/3y = 2
1/3x 1/2y = 13/6

Answer 1

hope this will help you

Answer 2

Answer:

Step-by-step explanation:

1/2x + 1/3y = 2......(1)

1/3x 1/2y = 13/6..........(2)

let 1/x be u and 1/y be v

so our equations become,

1/2u + 1/3v = 2                               1/3u + 1/2v = 13/6

(3u +2v)/6 =2                                 (2u + 3v)/6 = 13/6

3u + 2v =12  .......(3)                       2u + 3v = 13.............(4)

from (3),

3u + 2v =12

3u = 12-2v

u = (12-2v)/3

putting value of u in (4)

2u + 3v = 13

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

multiplying both sides by 3

3×2((12-2v)/3) + 3×3v = 13 ×3

2(12-2v) + 9v = 39

24 -4v +9v =39

5v = 39-24

5v = 15

v =15/5

v=3

putting v=3 in (3)

3u + 2v =12

3u +2(3) =12

3u+6 =12

3u=12-6

3u=6

u=6/3

u=2

hence v=3 and u =2

now,

      we know that,

   u = 1/x     v = 1/y

   2=1/x       3 = 1/y

   x= 1/2      y =1/3

therefore, value of x is 1/2 and value of y is 1/3 for the given equation

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