Step 1

$ \Delta = \begin{vmatrix} 4 & 5 \\ 8 & 10 \end{vmatrix} = 40-40=0$

The system may or maynot be consistent.

Step 2

$ \Delta_x = \begin{vmatrix} 9 & 5 \\ 18 & 10 \end{vmatrix} = 90-90=0$

$ \Delta_y = \begin{vmatrix} 4 & 9 \\ 8 & 18 \end{vmatrix} = 72-72=0$

$ \Delta = \Delta_x=\Delta_y=0 $ and $ \Delta$ has nonzero elements. $ \therefore $ the system is consistent with infinitely many solutions. It reduces to a single equation.

$ 4x+5y=9$

Step 3

Let $ x = t, t \in R$

Then $ y=\large\frac{9-4t}{5}$

The solution set is $ (x,y) = \bigg(t, \large\frac{9-4t}{5} \bigg), t \in R$