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 all, even