# 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
Inequalities systems and graphs 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
$$\displaystyle{y}\ge-{4}$$ An objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints.
b. Find the value of the objective function at each corner of the graphed region.
c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.
$$\displaystyle{z}={2}{x}+{3}{y}$$
$$\displaystyle{\left\lbrace\begin{array}{c} {x}{\quad\text{and}\quad}{y}\ge{0}\\{2}{x}+{y}\le{8}\\{2}{x}+{3}{y}\le{12}\end{array}\right.}$$ $$\displaystyle{x}+{y}\ge{5}{\left({1}\right)}$$
$$\displaystyle{x}\le{10}{\left({2}\right)}$$
$$\displaystyle{y}\le{5}{\left({3}\right)}$$
$$\displaystyle{x},{y}\ge{0}{\left({4}\right)}$$