Systems of Linear Inequalities Feasible Regions

Which system of linear inequalities represents the graph seen above?

• y≤ ½x - 1
  y > 2x - 4

• y > ½x - 1
  y ≤ 2x - 4

• y < ½x - 1
  y  ≥ 2x - 4

• y ≥ ½x - 1
  y < 2x - 4

Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function for this region.
3 ≤ y ≤ 6
y ≤ 3x + 12
y ≤ -2x + 6
f(x , y) = 4x - 2y

• The maximum value is 0 at (0, 6). The minimum value is - 20 at (-3, 3).

• The maximum value is 0 at (-3, 3). The minimum value is - 20 at (0, 6).

• The maximum value is 0 at (-2, 6). The minimum value is - 20 at (1.5, 3).

• The maximum value is 0 at (1.5, 3). The minimum value is - 20 at (-2, 6).

Solve the system of inequalities by graphing and describe regions of intersection.
y ≥ - 4x + 8
y < -4x + 4

• The graphs have an overlapping region below the first inequality and above the second inequality.

• The graphs have an overlapping region above the first inequality and below the second inequality.

• The regions of the inequalities entirely overlap.

• The graphs of the inequalities do not overlap, there is no solution to the system.

Select the correct graph for each inequality.

• A

• B

• C

• _D

Which system of inequalities is represented by the graph?

• x≤-2
  y≤x-3

• y≤-2
  y≤x-3

• x≥-2
  y≤x-3

• y≥-2
  y≤x-3

Feasible region

• the intersection of the graphs in a system of constraints

• written |x|, the distance the number is from 0 on a number line

• an apparent solution that must be rejected because it does not satisfy the original equation

• the process of finding the maximum or minimum values of a function for a region defined by inequalities

Which system of inequalities matches this graph?

• y≥-2x+3
  y≤x-3

• y>2x+3
  y≥x-3

• y>-2x+3
  y≥x-3

• y<-2x+3
  y≤x-3

Which system of inequalities is represented by this graph?

• y < -3x + 3 and y > -3x - 1

• y ≥ -3x + 3 and y ≤ -3x - 1

• y ≤ -3x + 3 and y ≥ -3x - 1

• y > -3x + 3 and y < -3x - 1

Which system of inequalities is shown?

• y ≥ -x - 1
  y < x + 4

• y < -x - 1
   y ≥ x + 4

• y > -x - 1
  y ≥ x + 4

• y > -x - 1
  y ≥ x + 3

Determine whether each ordered pair is a solution or not a solution to this system of inequalities.

y≥−x ​

2x+y>2

• Not a solution

• (4, -5)

• Not a solution

• (2,-2)

• Solution

• (5,6)

• Not a solution

• (2,3)

• Solution

• (0,0)