# Graph the feasible region for the system of inequalities y>4x-1 y<-2x+3

Question
Graph the feasible region for the system of inequalities
y>4x-1
y<-2x+3

2021-03-08
Step 1 Replace the inequality signs by equality signs and plot the two equations.
y>4x-1
y=4x-1 (1)
y
y=-2x+3 (2)
Now, check whether (0, 0) satisfies the inequalities.
If origin satisfies the inequality then the region containing origin is the region for inequality or vice-versa.
y>4x-1
For x=0:
4x-1=(4*0)-1=-1
As 0>-1, so y>4x-1 its true for (0,0).
Again, for x=0:
-2x+3=(-2*0)+3=3
As 0
Step 2 Plot the region of inequality and the region satisfying both the inequalities is the feasible region. The shaded region is the feasible region.

### Relevant Questions

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.
$$\displaystyle{z}={2}{x}+{3}{y}$$
$$\displaystyle{\left\lbrace\begin{array}{c} {x}{\quad\text{and}\quad}{y}\ge{0}\\{2}{x}+{y}\le{8}\\{2}{x}+{3}{y}\le{12}\end{array}\right.}$$
Graph the Inequalities, and shade the feasible region
$$\displaystyle{4}{x}+{5}{y}\ge{12}$$
$$\displaystyle-{x}+{2}{y}\ge{2}$$
Graph the feasible region for the system of inequalities
$$\displaystyle{y}{>}{4}{x}-{1}$$
$$\displaystyle{y}{<}-{2}{x}+{3}$$
Graph the solution set for the system of linear inequalities
$$\displaystyle{x}\ge{3}$$
$$\displaystyle{y}\ge-{1}$$
Graph the solution set of the system of inequalities.
$$\displaystyle{x}-{y}\le{2}{x}-{y}\le{2}$$
$$\displaystyle{x}\ge{3}$$
Consider the following system of linear inequalities.
$$\displaystyle{3}{x}+{4}{y}\le{12}$$
$$\displaystyle{4}{x}+{3}{y}\le{12}$$
$$\displaystyle{x}\ge{0}$$
$$\displaystyle{y}\ge{0}$$
graph, shade and find corner points.
Graph the solution set for the system of linear inequalities
x>-3
$$\displaystyle{y}\ge-{4}$$
$$\displaystyle{\left\lbrace\begin{array}{c} {x}\ge{0}{\quad\text{and}\quad}{y}\ge{0}\\{3}{x}+{y}\le{9}\\{2}{x}+{3}{y}\ge{6}\end{array}\right.}$$
$$\displaystyle{x}\ge{0},{y}\ge{0},{3}{x}+{y}\le{9},{2}{x}+{3}{y}\ge{6}$$