Step 1:

The first inequality is $4x +3y \leq 60$

Consider the equation $4x +3y =60$

The points $(15,0) $ and $(0,20)$ satisfy the equation .

The graph of the equation is drawn as shown.

The line divides the xy plane into two half planes.

Consider the point (0,0)

We see that, $ 4(0) +3(0) \leq 60$

=> $ 0 \leq 60$ is true.

Thus the inequality (1) is represented by the region below the line $4x+3y=60$ containing the point (0,0) (including the line )

Step 2 :

The second inequality is $ y \geq 2x$ -------(2)

Consider the equation $y=2x$

The points $(0,0) ,(2,4) $ satisfy the equation.

The graph of the line is drawn as shown.

The line divides the XY plane into two half planes.

Consider the point (1,0)

We see that, $ 0 \geq 2(1)$

$ 0 \geq 2$ is false.

Thus the inequality (2) is represented by the region above the line $y=2x$ not including the point (1,0) (including the line y=2x)

Step 3 :

The third inequality is $x \geq 3$ -------(3)

The inequality represents the region to the right of the line $x=3$ (including the line)

Step 4 :

The 4th inequality is $x,y \geq 0$

It represent the region in the first quadrant of the XY -plane including positive x-axis and positive y-axis.

Step 5:

Hence the solution of the system of linear inequalities is represented by the common shaded region including the points on the lines and y-axis.