1. Using Systems of Equations to Solve Problems A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation.

2. What is a system of equations??? A “system” of equations is a collection of equations with a same set of unknown variables.

3. System of Equations Not System of Equations OR

4. System of Equations Not System of Equations OR

5. System of Equations Not System of Equations OR

6. System of Equations Not System of Equations OR

7. System of Equations Not System of Equations OR

8. DefinitionNotes ExamplesNon-examples

9. System of Equations DefinitionNotes ExamplesNon-examples A “system” of equations is a collection of equations with a same set of unknown variables. Same variables in all equations More than one equation Only ONE equation!!! Equations don’t have same variables!!!

10. What does it mean to solve an equation? To “solve” an equation is to find the value(s) that replace the variable(s) and make the equation true.

11. To “solve a system of equations” means to determine what values will work for each variable in ALL equations.

12. Let’s create and solve some systems of equations…..

13. Find the value of two numbers if their sum is 12 and their difference is 2.

14. x + y = 12 x - y = 2 Let x be the first number Let y be the second number 0 1 2 3 7 12 11 10 9 5 11 10 9 7 9 8 7 5 12 10 The numbers are 7 and 5. xy x y

15. Find the value of two numbers if their sum is 10 and their difference is 1.

16. x + y = 10 x - y = 1 0 1 2 3 10 9 8 7 11 10 9 9 8 12 11 xy x y 5.5 4.5 5.5 4.5 The numbers are 5.5 and 4.5. Let x be the first number Let y be the second number

18. xy Graph the linear equations below and determine the solution to the system of equations by finding the intersection of the two lines. xy

20. 0 8 8 5 xy 0 5 10 15 4 7 10 13 xy Too difficult to tell exactly where intersection is!!

21. The moral of the story….. Sometimes it is not easy (or even possible!) to determine the solution to a system of equations by graphing the lines.

24. What do you notice about how the solutions to the systems of equations relate to the graphs of the equations? The solutions, if placed together as an ordered pair, form the coordinate of the intersection of the graphs of the two equations!!!!

25. System of Equations: y = 2 x + 2 y = x - 1 Solution to System: x = y = -3 -4