This document discusses solving systems of inequalities graphically. It provides examples of systems of inequalities and shows the steps to solve them graphically. The inequalities are written in set-builder form and then manipulated algebraically to isolate the variables. The solutions are represented graphically by shading the region defined by the intersecting inequalities. Examples are provided for students to work through in groups with solutions shown on subsequent slides. The document encourages using graph paper to solve the systems graphically.

1. 9.9 Systems of Inequalities
Ephesians 5:20 "Always giving thanks for all things in the
name of our Lord Jesus Christ to God, even the Father;"

2. Solve Graphically:
⎧5x + 2y ≤ 10
⎪8x + y < 8
⎪
⎨
⎪ x≥0
⎪ y ≥ 0
⎩

3. Solve Graphically:
⎧ 5
⎧5x + 2y ≤ 10 y ≤ − x + 15
⎪8x + y < 8 ⎪ 2
⎪ ⎪
⎨ ⎨ y < −8x + 8
⎪ x≥0 ⎪ x ≥ 0; y ≥ 0
⎪ y ≥ 0
⎩ ⎪
⎩

4. Solve Graphically:
⎧ 5
⎧5x + 2y ≤ 10 y ≤ − x + 15
⎪8x + y < 8 ⎪ 2
⎪ ⎪
⎨ ⎨ y < −8x + 8
⎪ x≥0 ⎪ x ≥ 0; y ≥ 0
⎪ y ≥ 0
⎩ ⎪
⎩
Graph & shade the region common to all.
Use graph paper!
(next slide for solution)

5. ⎧ 5
⎪ y ≤ − x + 15
2
⎪
⎨ y < −8x + 8
⎪ x ≥ 0; y ≥ 0
⎪
⎩

6. In your groups: ⎧ y > ( x − 3) − 2
⎪
2
⎨
⎪ y < x − 3
⎩
(solution is next)

7. In your groups: ⎧ y > ( x − 3) − 2
⎪
2
⎨
⎪ y < x − 3
⎩
(solution is next)

8. In your groups: 2
⎧−x + 4x > y + 5
⎨
⎩2x + 3y ≥ 14
(solution is next)

9. In your groups: 2
⎧−x + 4x > y + 5
⎨
⎩2x + 3y ≥ 14
(solution is next)
No Solution

10. HW #1
“Whatever you are by nature, keep to it, never
desert your line of talent. Be what nature
intended you for and you will succeed.”
Syndney Smyth