Question

Reduce them to a pair of linear equation 1/2x+1/3y=2​

Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

Let us assume 1/x = m and 1/y = n , then the equation will change as follows.

m/2 + n/3 = 2

⇒ 3m+2n-12 = 0…………………….(1)

m/3 + n/2 = 13/6

⇒ 2m+3n-13 = 0……………………….(2)

Now, using cross-multiplication method, we get,

m/(-26-(-36) ) = n/(-24-(-39)) = 1/(9-4)

m/10 = n/15 = 1/5

m/10 = 1/5 and n/15 = 1/5

So, m = 2 and n = 3

1/x = 2 and 1/y = 3

x = 1/2 and y = 1/3

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