# 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

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:

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.

### Relevant Questions

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 the inequality or system of inequalities.
$$\displaystyle{\left\lbrace\begin{array}{c} {x}\ge{0}{\quad\text{and}\quad}{y}\ge{0}\\{3}{x}+{y}\le{9}\\{2}{x}+{3}{y}\ge{6}\end{array}\right.}$$
Graph the solution set of system of inequalities:
$$\displaystyle{x}\ge{0},{y}\ge{0},{3}{x}+{y}\le{9},{2}{x}+{3}{y}\ge{6}$$
Graph the solution set of the system of inequalities or indicate that the system has no solution.
$$\displaystyle{\left\lbrace\begin{array}{c} {x}+{y}{>}{4}\\{x}+{y}{<}-{1}\end{array}\right.}$$
Graph the solution set of the system of inequalities or indicate that the system has no solution.
$$\displaystyle{\left\lbrace\begin{array}{c} {y}\ge{x}^{{2}}-{4}\\{x}-{y}\ge{2}\end{array}\right.}$$
Determine graphically the solution set for the system of inequalities:
$$\displaystyle{x}+{y}\le{4}$$
$$\displaystyle{2}{x}+{y}\le{6}$$
$$\displaystyle{2}{x}−{y}\ge−{1}$$
$$\displaystyle{x}\ge{0},{y}\ge{0}$$
Graph the solution set of the system of inequalities.
$$\displaystyle{x}-{y}\le{2}{x}-{y}\le{2}$$
$$\displaystyle{x}\ge{3}$$
Graph the solution set for the system of linear inequalities
x>-3
$$\displaystyle{y}\ge-{4}$$
$$\displaystyle{z}={2}{x}+{3}{y}$$
$$\displaystyle{\left\lbrace\begin{array}{c} {x}{\quad\text{and}\quad}{y}\ge{0}\\{2}{x}+{y}\le{8}\\{2}{x}+{3}{y}\le{12}\end{array}\right.}$$
$$\displaystyle{x}+{y}\ge{5}{\left({1}\right)}$$
$$\displaystyle{x}\le{10}{\left({2}\right)}$$
$$\displaystyle{y}\le{5}{\left({3}\right)}$$
$$\displaystyle{x},{y}\ge{0}{\left({4}\right)}$$