A) \[x=4,y=5\]
B) \[x=5,y=4\]
C) \[x=\frac{1}{4},\,y=\frac{1}{5}\]
D) None of these
Correct Answer: A
Solution :
Let \[\frac{1}{x+1}=u\]and \[\frac{1}{y-1}=v\], then the given |
pair of linear equations becomes |
\[5u-2v=\frac{1}{2}\] ...(i) |
and \[10u+2v=\frac{5}{2}\] ...(ii) |
On adding Eqs. (i) and (ii), we get |
\[15u=\frac{1}{2}+\frac{5}{2}\Rightarrow 15u=\frac{6}{2}\Rightarrow u=\frac{1}{5}\] |
On putting \[u=\frac{1}{5}\]in Eq. (i), we get |
\[5\times \frac{1}{5}-2v=\frac{1}{2}\Rightarrow v=\frac{1}{4}\] |
Now, \[u=\frac{1}{5}\Rightarrow \frac{1}{x+1}=\frac{1}{5}\] |
\[\Rightarrow \,x+1=5\,\,\Rightarrow x=4\] |
And \[v=\frac{1}{4}\Rightarrow \,\frac{1}{y-1}=\frac{1}{4}\Rightarrow y-1=4\Rightarrow y=5\] |
Hence, x = 4 and y = 5, which is the required unique solution. |
You need to login to perform this action.
You will be redirected in
3 sec