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# Solve for x and y: 5/(x+y)-2/(x-y)=-1, 15/(x+y)+7/(x-y)=10

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One of the most important and conceptual question from linear equations in two variables in which we have been asked to find the value of variables x and y from the equations 5/(x+y)-2/(x-y)=-1, 15/(x+y)+7/(x-y)=10

Kindly give me a detailed solution of this question

RS Aggarwal, class 10, chapter 3B, question no 27

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1. The given equations are

5/ x+y – 2/ x-y = -1 â€¦â€¦(i)

15/ x+y – 7/x-y= 10 â€¦â€¦(ii)Â  Substituting 1/x+y = u and 1/x-y = v in (i) and (ii), we get

5u â€“ 2v = -1 â€¦â€¦..(iii)

15u + 7v = 10 â€¦â€¦.(iv)

Multiplying (iii) by 3 and subtracting it from (iv), we get

7v + 6v = 10 + 3

â‡’13v = 13

â‡’v = 1

â‡’x â€“ y = 1 (âˆµ 1/ x-y = ) â€¦..(v)

Now, substituting v = 1 in (iii), we get

5u â€“ 2 = -1

â‡’5u = 1

â‡’u = 1/ 5

x + y = 5 â€¦â€¦.(vi)

Adding (v) and (vi), we get

2x = 6

â‡’ x = 3

Substituting x = 3 in (vi), we have

3 + y = 5

â‡’ y = 5 â€“ 3

= 2

Hence, x = 3 and y = 2.

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