This question is taken from linear equations in two variables in which we have been asked to find the value of 3/(x+y) + 2/(x-y) = 2 and 9/(x+y) – 4/(x-y) = 1
RS Aggarwal, Class 10, chapter 3F, question no 21
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Let 1/(x+y)=X and 1/(x−y)​=Y
3X+2Y=2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â …(i)
9X−4Y=1                       …(ii)
On multiplying (i) by 3 and (ii) by 1 and subtracting, we get
9X+6Y=6
−9​X+−​4Y=−1​​
10Y=5
∴Y=1/2​
On putting Y=1/2 in (i), we get
3X+2×1/2​=2
⇒X=1/3​
∴1/(x+y)=1/3​ and 1/(x−y)​=1/2​
⇒x+y=3                 …(iii)
x−y=2                      …(iv)
On adding (iii) and (iv), we get
2x=5
⇒x=5/2​
On putting x=25​ in (iii), we get
5/2​+y=3
⇒y=3−5/2​=1/2​
∴x=5/2​, y=1/2​