3.3 Graphing and Solving Systems of Linear Inequalities

Dashed or Solid If an inequality has a, then draw a dashed line. If an inequality has a, then draw a solid line.

Shading If an inequality has a < or ≤, shade below the line. If an inequality has a > or ≥ shade above the line. Use a test point that is NOT on the line to check: (0,0) (1,0) etc.

Example: y < x + 3 Line is dashed because it is <, Plug in (0,0) as a test point: 0 < 0+3 Since 0<3, the point (0,0) is included in the shaded area. The area is shaded below the line. slope is 1, y intercept is at (0,3)

Let’s add another inequality to the same grid with y -2x - 3 Which side of y > -2x-3 should be shaded? Plug in (0,0) to check. It should be shaded to the right.

y -2x - 3 The solution to this system of inequalities is the area where the two shaded areas overlap.

y > -x + 2 y ≤ 2x + 1

Determine if the point is a solution to the system of inequalities: A: (-3,2) B: (5,1) C: (0,7)

Solving a system of inequalities y > 2x + 3 y < 4x - 1

Solving a system of inequalities y > 2x + 3 y < 4x - 1

Solving a system of inequalities y ≥ - 2 y < 1

Solving a system of inequalities y ≥ 2x x < 1

Classwork / Homework Text page 153, #11-21 All

Solving a system with absolute value inequalities y < 3 y > |x-1|

Solving a system with absolute value inequalities y > ½ x - 5 y ≤ - |x-2| + 1