Step 1:

The first inequality is $ x-2y \leq 3$

Consider the equation $x-2y =3$

The points $(3,0) $ and $(0,-3/2)$

The graph of the line is drawn as shown.

The line divides the XY plane into two half planes.

Consider the point $(0,0)$

We see that $0-2(0) \leq 3$

=> $ 0 \leq 3$ is true.

Thus the inequality $x-2y \leq 3$ is represented by the region above the line $x-2y =3$ containing the point (0,0) (including the line)

Step 2:

The second inequality is $3x+4y \geq 12$------(2)

Consider the equation $3x+4y=12$

we see that the points (4,0) and (0,3) 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 $3(0) +4(0) \geq 12$

=> $ 0 \geq 12$ is false.

Thus the inequality (2) is represented by the region below the line $3x+4y=12$ containing the point (0,0)

Step 3:

The third inequality is $x \leq 0$ -----(3)

It is represented by the region to the right of y axis including the y- axis.

Step 4:

The 4th inequality is $y \geq 1$---------(4)

Consider equation $y=1$

The graph is drawn as shown . The inequality (4) represents the region above the line $y=1$ (including the line y=1)

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.