# 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

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
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Step 1
For the inequalities we make auxiliary equations.
x=0 ,x+y=4, 2x+y=5
$x\ge 0$
$x+y\le 4$
$2x+y\le 5$
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 $x\ge 0$, shade the right side of x=0
For $x+y\le 4$, shadetowards (0,0) because x=0, y=0 satisfies the inequality.
For $2x+y\le 5$, shade towards (0,0) because x=0, y=0 satisfies the inequality.
So the common region is the shaded region in black.