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
The given equations are
5/ x+y – 2/ x-y = -1 ……(i)
15/ x+y – 7/x-y= 10 ……(ii) Substituting 1/x+y = u and 1/x-y = v in (i) and (ii), we get
5u – 2v = -1 ……..(iii)
15u + 7v = 10 …….(iv)
Multiplying (iii) by 3 and subtracting it from (iv), we get
7v + 6v = 10 + 3
⇒13v = 13
⇒v = 1
⇒x – y = 1 (∵ 1/ x-y = ) …..(v)
Now, substituting v = 1 in (iii), we get
5u – 2 = -1
⇒5u = 1
⇒u = 1/ 5
x + y = 5 …….(vi)
Adding (v) and (vi), we get
2x = 6
⇒ x = 3
Substituting x = 3 in (vi), we have
3 + y = 5
⇒ y = 5 – 3
= 2
Hence, x = 3 and y = 2.