Question
Solve the following simultaneous equation.
99x + 101 y = 499; 101x + 99y = 501
99x + 101 y = 499; 101x + 99y = 501
✓
Answer
$\begin{aligned}
& 99 x+101 y=499 \ldots \\
& 101 x+99 y=501 \ldots
\end{aligned}$
Adding both the Equations
$\begin{aligned}
99 x+101 y & =499 \\
101 x+99 y & =501 \\
200 x+200 y & =1000
\end{aligned}$
Dividing both sides by 200
$x+y=5$
Subtract equation (I) and (II)
$\begin{gathered}
99 x+101 y=499 \\
-101 x-99 y=-501 \\
\hline-2 x+2 y=-2
\end{gathered}$
Divide both sides by $(-2)$
$x-y=1 .... (iv)$
Equating Eq. (III) and (IV)
$\begin{aligned}
& x+y=5 \\
& \frac{x-y=1}{2 x=6} \\
& x=\frac{6}{2} \\
& x=3
\end{aligned}$
Substituting $x=3$ in Eq. III
$\begin{aligned}
& 3+y=5 \\
& y=5-3 \\
& y=2
\end{aligned}$
$\therefore$ solution is $( x , y )=(3,2)$
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