Draw the graph of the solution set of the system of inequations `2x+3yle 4, xge0and y ge 0.`

Explanation

Consider the equations
`2x+3y=6,x+4yle4,x=0and y=0.`
Now, `2x+3y=63impliesx/3+y/2=1.`

This line meets the axes at `A(3,0)and B(2.,).` Join these points and draw a thick line. Clearly, the portion not containing (0,0) represents the solution set of the inequation `2x+3yge6.` Again, `x+4y=4impliesx/4+y/1=1.`
This line meets the axes at `C(4,0)and D(0,1).` Join these points and draw a tick line. Clearly the portion containing (0,0) represents the solution set of the inequation `x+4yle4.`
Clearly , `x ge0` is represented by the y-axis and the portion on its right-hand side.
Also, `yge0` is represented by the x-axis and the portion above the x-axis.
Hence, the shaded ragion represents the solution set of the given inequations.