Question
Solve the following simultaneous equations.
$\frac{148}{x}+\frac{231}{y}=\frac{527}{x y} ; \frac{231}{x}+\frac{148}{y}=\frac{610}{x y}$
$\frac{148}{x}+\frac{231}{y}=\frac{527}{x y} ; \frac{231}{x}+\frac{148}{y}=\frac{610}{x y}$
✓
Answer
$\frac{148}{x}+\frac{231}{y}=\frac{527}{x y} \Rightarrow \frac{148 y+231 x}{x y}=\frac{527}{x y} \Rightarrow 231 x+148 y=527 \ldots(I) $
$\frac{231}{x}+\frac{148}{y}=\frac{610}{x y} \Rightarrow \frac{231 y+148 x}{x y}=\frac{610}{x y} \Rightarrow 148 x+231 y=610 \ldots(II)$
Adding Eq. I and II
$379 x+379 y=1137$
$x+y=3\dots(III)$
Subtracting Eq. I and II
$83 x-83 y=-83 $
$x-y=-1 \ldots( IV )$
Equating I and II
$x+y=3 $
$x-y=-1 $
$2 x=2 $
$x=\frac{2}{2} $
$x=1$
Substituting $x=1$ in Eq. I
$1+y=3 $
$y=3-1 $
$y=2$
Hence, $(x, y)=(1,2)$
$\frac{231}{x}+\frac{148}{y}=\frac{610}{x y} \Rightarrow \frac{231 y+148 x}{x y}=\frac{610}{x y} \Rightarrow 148 x+231 y=610 \ldots(II)$
Adding Eq. I and II
$379 x+379 y=1137$
$x+y=3\dots(III)$
Subtracting Eq. I and II
$83 x-83 y=-83 $
$x-y=-1 \ldots( IV )$
Equating I and II
$x+y=3 $
$x-y=-1 $
$2 x=2 $
$x=\frac{2}{2} $
$x=1$
Substituting $x=1$ in Eq. I
$1+y=3 $
$y=3-1 $
$y=2$
Hence, $(x, y)=(1,2)$
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