1. Systems of Equations/Inequalities
Module 4
Systems of Equations/Inequalities

3. 4.01 – Solve by graphing – 14 points
Answer: (x,y) where the two lines cross
Different slopes
Consistent & independent
Answer: no solution
Same slopes with a different y-intercept
Inconsistent
Answer: infinitely many
Same slopes with the same y-intercept
Consistent & dependent

4. Definitions Consistent – equations intersect
Inconsistent – no solution
Independent – finite (limited) number of solutions
Dependent – infinite (no limit) number of solutions

5. How to solve by graphing
Put each equation in slope intercept form (y=mx+b)
Graph both equations on the same graph
Determine the solution. If there is one, you must name it ‘(x,y)’ where they cross. If there is none, then the answer is ‘no solution.’ If there are infinitely many, then the answer is ‘infinitely many.’

6. Solving Linear Equations Using Graphing
Video Example
Solving Linear Equations Using Graphing

7. 4.02 Solve by Substitution – 15 points

8. Example #1

9. Example #2

10. Word problems Use the words to write your own two equations
Use the answers they give you when you need help
Example:

11. Solving Linear Systems Using Substitution
Video Example
Solving Linear Systems Using Substitution

12. 4.03 Solve by Elimination
Addition
Using

13. Addition
Using

14. Multiplication
Using

15. Multiplication
Using

16. Solving Linear Systems Using Elimination
Video Example
Solving Linear Systems Using Elimination

17. 4.04 System of Inequalities
When you graph the equations using Desmos or by hand, chose the areas that are shaded by both equations
If you aren’t sure about a point (if it is included in the solution, or the shaded part) you can test it by plugging it in to both equations (x & y) and see if the equation is true

18. Graphing Inequalities
Before you graph systems of inequalities, you must know how to first graph one inequality.

21. Solving Systems of Inequalities
Video Example
Solving Systems of Inequalities

22. 4.05 Linear Programming
Use a graphing program or graph by hand to plug in the equations
You will have multiple lines and you will need to know what your vertices of the feasible region are
The feasible region is the part of the graph that is shaded by all of the equations you have or where they intersect
Vertices
Feasible region

23. One purpose of linear programming is to find out how to maximize profit or minimize cost for a business
Once you have graphed your system of inequalities and found the vertices, you will plug those values in to your objective function to find your max or min value

26. Linear Programming Basics
Video Examples
Linear Programming Basics
Linear Programming Word Problem