4.3.1 – Systems of Inequalities

• Recall, we solved systems of equations

• What defined a system?

• How did you find the solutions to the system?

Systems of Inequalities

• A system of linear inequalities has 2 or more linear inequalities

• Their solutions are any ordered pair that satisfies BOTH inequalities

• Only method to solve? Graphing

Solutions

• To test whether a particular solution, or solution set (x,y) is a solution, we plug the x and y solutions and test both inequalities

• Example. Check whether (3, -1) is a solution to the system:

• x + y > 1• y < 2

• Example. Tell whether (4, 2) is a solution to the system:

• x + y ≤ 2• 4x – y > 3

• Example. Tell whether (4, 2) is a solution to the system:

• x > 1• x + y ≤ 4

Solving Systems

• Similar to solving equations, to solve a linear system, we will graph both inequalities on the same plane

• Remember…• <, > = Dashed Line• ≤, ≥ = Solid Line• >, ≥ = Shade Above (when not in std. form)• <, ≤ = Shade Below (when not in std. form)

• Solutions?

• The solutions are where the shading will overlap

• Helpful to have 2 colors

• To check your solution, choose a test point in the overlapping shaded region

• Example. Find the solutions to the system• y < 2x – 3• y ≥ -x - 1

• Example. Find the solutions to the system• y ≤ x - 4• x ≥ -8

• Example. Find the solutions to the system• y ≤ -x + 5• x – y < 4

• Example. Find the solutions to the system• x + y > 4• 2x – y ≥ 3

• Assignment• Pg. 188• 3-8 all, 10-18 even