Question
solve :
$\frac{4}{x}+\frac{5}{y}=7 ; \frac{3}{x}+\frac{4}{y}=5$
$\frac{4}{x}+\frac{5}{y}=7 ; \frac{3}{x}+\frac{4}{y}=5$
✓
Answer
$\begin{aligned}
& \frac{4}{x}+\frac{5}{y}=7 ; \frac{3}{x}+\frac{4}{y}=5 \\
& 4\left(\frac{1}{x}\right)+5\left(\frac{1}{y}\right)=7 \ldots \text { (I) } \\
& 3\left(\frac{1}{x}\right)+4\left(\frac{1}{y}\right)=5 \ldots \text { (II) }
\end{aligned}$
Replacing $\left(\frac{1}{x}\right)$ by $m$ and $\left(\frac{1}{y}\right)$ by $n$ in equations (I) and (II), we get
$\begin{array}{lll}
4 m+5 n=7 \ldots & \text { (III) } \\
3 m+4 n=5 \ldots & \text { (IV) }
\end{array}$
On solving these equations we get
$m=3, n=-1$
Now, $m=\frac{1}{x} \quad \therefore 3=\frac{1}{x} \quad \therefore x=\frac{1}{3}$
$n=\frac{1}{y} \quad \therefore-1=\frac{1}{y} \quad \therefore y=-1$
$\therefore$ Solution of given simultaneous equations is $(x, y)=\left(\frac{1}{3},-1\right)$
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