1. Warm Up
Solve the following system of equations using any method:

2. Systems Of
Equation
Word Problems

3. Word Problems
When working with system-of-equations word problems, determine the two equations that you can write.
Then solve using any method

4. Example 1
A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

5. Example 2
The senior classes at Knightdale High School and Enloe HS planned separate trips to New York City. The senior class at KHS rented and filled 1 van and 6 buses with 372 students. EHS rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

6. Example 3
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.

7. Graphing
Linear
Inequalities

8. We show the solution to a linear inequality with a graph.
Step 1) Put the inequalities into slope-intercept form.
y = mx + b
slope
y-intercept

9. Step 2) Graph the line
If the inequality is < or >, make the lines dotted.
If the inequality is < or >, make the lines solid.

10. Step 3) Shade the correct region of the graph:
a) Above the line for y > or y .
b) Below the line for y < or y ≤.
**This is because more then 1 ordered pair can be a solution!

11. Examples:
1) y > -5x + 4

12. Examples:
2) x < ) y ≥ -3

13. Careful when you divide by a negative!
Examples:
4) 2x – 3y ≤ 6
Careful when you divide by a negative!

14. Examples:
5) 3x + 2y < -2

15. Systems of
Inequalities

16. We show the solution to a system of linear inequalities with a graph!

17. Steps to Graphing a System of Inequalities:
Put the inequalities into slope-intercept form.
Decide if the lines should be dotted or solid.
Shade above for y > or y , shade below for y < or y ≤.
Shade the overlapping section darker to show where the solutions to both inequalities lie.

18. Example #1: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form:

19. Graph each line, make dotted or solid and shade the correct area.
shade above
dotted
shade below

20. #2 Graph the system of linear inequalities.
x ³ –1
y > x – 2

21. #3 x > -2 y < 6 -2x + y > -5

22. Class Work
Graph the System of Inequalities on the handout

23. Homework
HW 2.4