Question

20.
Solve the pairs of linear equations by the method of eleminatic
4/x+ 5/y= 7, 5/x+4/y= 13/2​

Answer 1

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Answer 2

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Given ,

The pair of linear equations are

4/x + 5/y = 7

5/x + 4/y = 13/2

Let , 1/x = u and 1/y = v , Then

4u + 5v = 7 ---- (i)

5u + 4v = 13/2 ---- (ii)

Multiply eq (i) by 5 and eq (ii) by 4 , we get

20u + 25v = 35 ---- (iii)

20u + 16v = 26 ---- (iv)

Subtract eq (iv) from eq (iii) , we get

( 20u + 25v ) - (20u + 16v) = 35 - 26

25v - 16v = 9

9v = 9

v = 1

Put the value of v in eq (iv) , we get

20u + 16 = 26

20u = 26 - 16

20u = 10

u = 1/2

Now , substitute the values of v and u in 1/x = u and 1/y = v , we get

1/x = u

1/x = 1/2

x = 2

and

1/y = v

1/y = 1

y = 1

Hence , the values of x and y are 2 and 1

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