Graphing Systems of Inequalities



Graphing Systems of Inequalities 5B

            When we solved and graphed inequalities with only one variable (ex: x > 3), we moved on to compound inequalities (AND/OR).  We would graph both inequalities on the same number line and decide what to keep based on whether it was an AND or an OR problem.  When we graphed linear equations on the coordinate plane we moved on to solving systems of equations graphically.

When we graph inequalities in two variables on the coordinate plane, we do not graph compound inequalities.  We move on to solving systems of inequalities.  It takes a little from both inequalities with one variable and solving systems graphically.

Solve the system of inequalities graphically:

                        y > ¼ x + 3

                        y < 3x – 5

Step 1:  Step 2: ON THE SAME GRAPH

Graph and shade the 1st inequality              Graph and shade the 2nd inequality

    y > ¼ x + 3                                                                  y < 3x – 5

m = [pic] = [pic]                                                      m = [pic]= [pic]

1st pt= (0,3)                                                                   1st pt.= (0,-5)

 (0, 2)                          (0, 4)                                 (0-6)                                      (0,-4)

y > ¼ x + 3 y > ¼ x + 3 y < 3x – 5 y < 3x – 5

2 > ¼ (0)+3          -3 > ¼ (0) + 3                     -6 < 3(0) - 5                            -4 < 3(0) - 5    

2  >  3                         4 > 3                               -6 < -5                              -4 < -5

 FALSE                     TRUE                                    TRUE                                      FALSE

Step 3: Label the area where the shading intersects with an “S”

                                                                                               

1) y < ⅓x – 4   2) 4x + 2y ≤ 4

    y > -5x + 1 5x – 3y < 9

3) 2x + 12y > 36 4) x ≥ 4

11x – 33y ≥ 66 (y – 3) > [pic](x – 2)

5) 42x – 14y < 56 6) (y – 2) > [pic](x – 4)

y ≥ -2 15x + 9y ≤ 27

Name ______________________________________ Date _____________

Algebra I – Pd ____ Graphing Systems of Linear Inequalities

Graph the following systems, show all work on looseleaf

1) y≥ 3x + 1 2) 2y≥ x – 4

y – 1 < x y < 3x

3) -2y ≥ -4x – 6 4) x + y > 6

y ≥ x y ≤ 2x – 5

5) y – 4 > -2x 6) 2x – y ≤ 3

y > x + 2 3x + y ≤ 7

7) y > -2x + 10 8) y ≤ x -3

3x + y < 7 -y – x < -1

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