3-11 System of Linear Inequalities.notebook May 06, 2016

3-11 System of Linear Inequalities 1

There are 4 slices of the pie. Which one is the correct slice or area??

3-11 System of Linear Inequalities.notebook May 06, 2016

3-11 System of Linear InequalitiesEx 1:

Step1: Isolate y in both inequalities.

+3x

y < 3x - 2 -y 2x - 3

-1 -1 -1

y -2x + 3

SWITCH SIGN!!!

Step2: Graph both lines. Do not shade yet.

Step3: Pick any point in each section of the pie.

+3x +2x +2x

Sketch the solution to the system of inequalities.

3-11 System of Linear Inequalities.notebook May 06, 2016

0 3 0 -2(0) + 3

3-11 System of Linear Inequalities

Ex 1: -continued

Step4: Identify each of the 4 points.

Where is the green point? (0, 0)Where is the blue point? (1, -2)Where is the yellow point? (1, 3)Where is the pink point? (3, 1)

Step5: To test each point. Plug each point into each equation.

(0, 0)

0 < 3(0) - 2 0 < - 2

YES!!!!!

NO!!!!!

NO!!!!!

(1, -2)

-2 1 -2 -2(1) + 3

-2 < 3(1) - 2 -2 < 1 NO!!!!!

Note: They must both be "yes" for this to be correct.

(1, 3)

Note: They must both be "yes" for this to be correct.

YES!!!!!3 1 3 -2(1) + 3

3 < 3(1) - 2 3 < 1 NO!!!!!

Note: They must both be "yes" for this to be correct.

(3, 1)

YES!!!!!

1 -3 1 -2(3) + 3

1 < 3(3) - 2 1 < 7

Note: They must both be "yes" for this to be correct.

YES!!!!!

Shade the correct region or correct piece of pie.

ANSWER

3-11 System of Linear Inequalities.notebook May 06, 2016

3-11 System of Linear InequalitiesChecks for Example 1Sketch the solution to each system of inequalities.

(-1, 1)

(-2, 0)

3-11 System of Linear Inequalities.notebook May 06, 2016

53-11 System of Linear InequalitiesChecks for Example 1: - continuedSketch the solution to each system of inequalities.

(0, 0)

(-1, -1)

y -4x +2y x - 3

y -4x -3y 2x +3