Question:
$x+2 y=5$
$3 x+6 y=15$
Solution:
Using the equations, we get
$D=\left|\begin{array}{cc}1 & 2 \\ 3 & 6\end{array}\right|=6-6=0$
$D_{1}=\left|\begin{array}{cc}5 & 2 \\ 15 & 6\end{array}\right|=30-30=0$
$D_{2}=\left|\begin{array}{cc}1 & 5 \\ 3 & 15\end{array}\right|=15-15=0$
$\therefore D=D_{1}=D_{2}$
Hence, the system of linear equation has infinitely many solutions.
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