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

Question
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

Answers (1)

2021-02-01
Step 1
For the inequalities we make auxiliary equations.
x=0 ,x+y=4, 2x+y=5
x>=0
\(\displaystyle{x}+{y}\le{4}\)
\(\displaystyle{2}{x}+{y}\le{5}\)
x=0
x+y=4
2x+y=5
Step 2
Then we make table for the equations and graph:
image
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 \(\displaystyle{2}{x}+{y}\le{5}\), shade towards (0,0) because x=0, y=0 satisfies the inequality.
So the common region is the shaded region in black.
0

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