Graph the solution set of each system if inequalities. X is greater than or = 0 X+Y is less than or equal to 4 2x+y is less than or equal to 5

Step 1
For the inequalities we make auxiliary equations.
x=0 ,x+y=4, 2x+y=5
$x\ge 0$
${\displaystyle x+y\le 4}$
${\displaystyle 2x+y\le 5}$
x=0
x+y=4
2x+y=5
Step 2
Then we make table for the equations and graph:

Step 4
Then shade the regions according to the inequalities.
For ${\displaystyle x\ge 0}$, shade the right side of x=0
For ${\displaystyle x+y\le 4}$, shadetowards (0,0) because x=0, y=0 satisfies the inequality.
For ${\displaystyle 2x+y\le 5}$, shade towards (0,0) because x=0, y=0 satisfies the inequality.
So the common region is the shaded region in black.