Step 1:

Consider the first inequality $3x+4y \leq 60$ ---------(1)

Let corresponding the equation see $3x +4y =60$

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

The graph of the equation is drawn as shown .

The line divides the xy- plane into two half planes.

Consider the points $(0,0)$

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

$0 < 60$ is true.

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

Step 2:

The second inequality is $x +3y \leq 30$

Consider the equation $x+3y =30$

The points (30,0) and (0,15) satisfy the equation .

The graph of this line is drawn as shown .The line divides the x-y into two half - planes.

Consider point (0,0). We see that , Thus the inequality represent the region below the line $x+3y =30$ containing the point (0,0) (including the line x+3y=30)

Step 3:

The third inequality is $x \geq 0$

It represent the region to the right of the y axis including y axis.

Step 4:

The fourth inequality is $y \leq 0$

It represented the region above the x-axis including the x axis

Step 5 :

The given system of linear inequalities represents the common shaded region including all the lines.