Warm-Up

1
Warm-Up

• What is a system of equations?
• How can you find a solution to a system of
  equations using a graph?
• Graph the inequality y lt 3x 1.

2
Section 7.6 Solving systems of inequalities

• SWBAT solve a system of linear inequalities by
  graphing

3
System of linear inequalities

• Two or more linear inequalities given together

4
solutions

• A solution of a system of linear inequalities is
  an ordered pair that is a solution of each
  inequality in the system.

5
Solving By graphing

• Put in slope-intercept form
• Graph each inequality in the coordinate plane
• Shade the intersection (overlap) of all the
  inequalities

6
Example

• Graph the system of linear inequalities
• y lt 2
• x 1
• y gt x 2
• Label each vertex
• of the solution area

7
Example

• Graph the system of linear inequalities
• x 0
• y 0
• y 2
• x 2y 6
• Label each vertex
• of the solution area

8
Example

• Write a system of inequalities that defines the
  shaded region below

9
Example

• Plot the points and draw line segments connecting
  the points to create the polygon. Then write a
  system of linear inequalities that defines the
  polygonal region.
• Triangle (0, 0),
• (-7, 0), (-3, 5)