Solve the following pair of equations by reducing them to a pair of linear equations: |
\[\frac{1}{x}-\frac{4}{y}=2\] |
\[\frac{1}{x}+\frac{3}{y}=9\] |
Answer:
Given, \[\frac{1}{x}-\frac{4}{y}=2\] \[\frac{1}{x}+\frac{3}{y}=9\] Let \[\frac{1}{x}=u,\frac{1}{y}=v\] So, \[u-4v=2\] ?(i) \[u+3v=9\] ?(ii) On solving eq. (i) and eq. (ii) \[_{\begin{smallmatrix} u\,\,+\,\,3v\,\,=\,\,9 \\ -\,\,\,\,\,\,\,\,\,- \\ \overline{\,\,\,\,\,-7v\,\,=\,\,-7} \end{smallmatrix}}^{u\,\,-\,\,4v\,\,=\,\,2}\] \[v=1\] Putting the value of v in eq. (i) \[u-4v=2\] \[u-4\times 1=2\] \[u-4=2\] \[u=2+4\] \[u=6\] So \[v=1\Rightarrow \frac{1}{y}=1,y=1\] \[u=6\Rightarrow \frac{1}{x}=6,x=\frac{1}{6}\] Hence, \[x=\frac{1}{6}\] and \[y=1\]
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