Question

x + 2y = 5
3x + 6y = 15

Answer 1

Using the equations, we get
\[D = \begin{vmatrix}1 & 2 \\ 3 & 6\end{vmatrix} = 6 - 6 = 0\] 
\[ D_{1 =} \begin{vmatrix}5 & 2 \\ 15 & 6\end{vmatrix} = 30 - 30 = 0\] 
\[ D_2 = \begin{vmatrix}1 & 5 \\ 3 & 15\end{vmatrix} = 15 - 15 = 0\] 
\[\therefore D = D_1 = D_2\]
Hence, the system of linear equation has infinitely many solutions.