Solve for x and y:

and y ≠ 1

We have


and


where x≠ - 1 and y≠1


Lets simplify these equations. Assuming p = 1/(x + 1) and q = 1/(y – 1),



5p – 2q = 1/2


10p – 4q = 1 …(i)


Also,


10p + 2q = 5/2


20p + 4q = 5 …(ii)


To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.


The variable q in both the equations have same coefficient.



30p = 6


p = 1/5


Substitute p = 1/5 in eq.(i)/eq.(ii), as per convenience of solving.


Thus, substituting in eq.(i), we get


10(1/5) – 4q = 1


2 – 4q = 1


4q = 2 – 1 = 1


q = 1/4


Thus, p = 1/5 and q = 1/4


As p = 1/(x + 1),



x + 1 = 5


x = 4


And q = 1/(y – 1)



y – 1 = 4


y = 5


Hence, we have x = 4 and y = 5


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