Question

5/x+1 - 2/y-1 = 1/2
10/x+1 - 2/y-1 = 5/2

reduce them to pair of linear equations!!​

Answer 1

Given equations are-

5/x+1 - 2/y-1 = 1/2 ---eq(1)

And,

10/x-1 - 2/y-1 = 5/2----eq(2)

Let 1/x+1 = p and 1/y-1 = q

By Putting the values of x and y in eq(1) and eq(2) we get--

5p - 2q = 1/2

Or, 10p - 4q = 1 ---eq(3)

{transporting 2 towards LHS}

10p - 2q = 5/2

Or, 20p - 4q = 5-----eq(4)

{transporting 2 towards LHS}

Therefore the given equations are now reduced to pair of linear equation {eq(3) and eq(4)} now we can solve it easily.

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Answer 2

Answer:

Let 1/x+1 = m

1/y-1 = n

Equations:

5m - 2n = 1/2

10m - 2n = 5/2

Solution:

=> 5m - 2n = 1/2

=> 10m - 4n = 1

=> m = (1 + 4n)/10

10m - 2n = 5/2

=> 20m - 4n = 5

Put value of m:

=> 2 + 8n - 4n = 5

=> 4n = 3

=> n = 3/4

m = (1 + 4n)/10 = (1 + 3)/10

=> m = 4/10 = 2/5

m = 1/x+1 = 2/5

=> 5 = 2x + 2

=> 2x = 3

=> x = 3/2

n = 1/y-1 = 3/4

=> 4 = 3y - 3

=> 7 = 3y

=> y = 7/3

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