Question
Solve the following simultaneous equation.
5x + 2y = –3; x + 5y = 4
5x + 2y = –3; x + 5y = 4
✓
Answer
$\begin{aligned}
& 5 x+2 y=-3 \ldots(1) \\
& x+5 y=4 \ldots (2)
\end{aligned}$
Multiply Eq. I by 5 and Eq. II by 2
$\begin{aligned}
& 25 x+10 y=-15 \ldots \text { (III) } \\
& 2 x+10 y=8 \ldots \text { (IV) }
\end{aligned}$
Change sign of Eq.(IV)
$\begin{gathered}
25 x+10 y=-15 \\
-2 x-10 y=-8 \\
\hline 23 x=-23
\end{gathered}$
$\begin{aligned}
& x=-\frac{23}{23} \\
& x=-1
\end{aligned}$
Subsituting $x=-1$ in Eq.II
$\begin{aligned}
& -1+5 y=4 \\
& 5 y=4+1 \\
& 5 y=5 \\
& y=\frac{5}{5} \\
& y=1
\end{aligned}$
$\therefore$ solution is $( x , y )=(-1,1)$
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