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