Solve the following simultaneous equation. 49x – 57y = 172; 57x –… - Vidyadip

Question

Solve the following simultaneous equation.
49x – 57y = 172; 57x – 49y = 252

✓

Answer

$\begin{aligned}
& 49 x-57 y=172 \ldots \\
& 57 x-49 y=252 \ldots
\end{aligned}$
Adding both the Equations
$\begin{gathered}
49 x-57 y=172 \\
57 x-49 y=252 \\
\hline 106 x-106 y=424
\end{gathered}$
Dividing both sides by 106
$x-y=4$
Subtract equation (I) and (II)
$\begin{aligned}
49 x-57 y & =172 \\
-57 x+49 y & =-252 \\
\hline-8 y-8 y & =-80
\end{aligned}$
Divide both sides by $(-8)$
$x+y=10$
Equating Eq. (III) and (IV)
$\begin{aligned}
& x-y=4 \\
& \frac{x+y=10}{2 x}=14 \\
& x=\frac{14}{2} \\
& x=7
\end{aligned}$
Substituting $x=7$ in Eq. IV
$\begin{aligned}
& 7+y=10 \\
& y=10-7 \\
& y=3
\end{aligned}$
$\therefore$ solution is $( x , y )=(7,3)$

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