The first inequality is $ 5x+4y \leq 20$ ----------(1)
Consider the equation $5x+4y =20$
The point $(4,0) $ and $(0,5) $ satisfy the equation.
The graph of this line is drawn as shown.
The line divides the xy - plane into two half planes .
Consider the point (0,0)
We see that $5(0) +4(0) \leq 20 $
$0 \leq 20$ is true.
Thus the region inequality represents the region below the line $5x+4y=20$ containing the point (0,0) (including the line)
The second inequality is $ x \geq 1$ ---(2)
Consider the $x=1$ . The graph of the line is as shown.
The inequality represents the region on the right hand side of the line $x=1$ (including the line x=1)
The third inequality is $ y \geq 2$
Consider y=2 . The graph is as shown.
The inequality represents the region above the line $y=2$ (including the line y=2)
Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the lines.