Welcome to September! Please do the following: Pick up Entry Ticket and U2L1 from the side shelf. Write homework in your agendas (I will not pass out assignment list) Homework: HW #1 Pg. 71 #11-31 odd, 32 (15, 17, 19 graphing calc.) HW #2 Pg. 76 #9-15 odd Finish Project Updates: 1 Question Graphing Calculator Quiz 2.1 1/5 periods on 9/4 6 period on 9/5 2 mins 1/5° Due – 9/4 6° Due – 9/5

Agenda Entry Ticket U2L1 Wartime Battle U2L1 Continued… Cool-Down… All tests will be returned once all students have taken it! If you have not taken the test, please come see me so we can schedule a time. 1 min

Entry Ticket 1 min

Learning Objective By the end of this period you will be able to: Solve systems of equations algebraically and graphically.

Solving Systems of Equations in Two Variables (2.1) System of Equations A set of two or more equations. To solve a system of equations means to find values for the variables in the equations which make all the equations true. Methods for solving systems of equations are: substitution, elimination, and graphing.

Solving Systems of Equations in Two Variables (2.1) In the last unit we learned how to graph a linear equation. Now, graph two linear equations on the same graph and determine the solution (an ordered pair). How would you classify the lines in (a)-(c) ? Now that we are in pre-calculus, we have a more academic name for these types of lines!

Solving Systems of Equations in Two Variables (2.1)

Solving Systems of Equations in Two Variables (2.1) We will come across some systems where the solution could more easily be found using a device and this device is our calculator! Steps for Graphing on a Calculator: Press y = Type in your equation 3x + 2 Press Zoom Since this equation is simple we know it will not exceed a graph from -10 to 10, press ZStandard; this makes your calculator window go from -10 to 10.

Solving Systems of Equations in Two Variables (2.1) Steps for Graphing on a Calculator: Press y = Type in your equation 3x + 50 Press Zoom Since this equation is more difficult it will exceed a graph from -10 to 10, press ZoomFit; this makes your calculator window see whatever you are graphing. Usually on a grah we want to see the x and y-axis. You must play with the window. Press Window. Adjust your window such that you can see the x and y-axis. Also adjust the Xscl (what you are counting by on the x-axis) and Yscl (what you are counting by on the y-axis).

Solving Systems of Equations in Two Variables (2.1) Take 8 minutes to attempt the calculator exploration. This exploration will be very similar to the format of your 1 question quiz.

Wartime Battle During war games, it is your job to navigate one of our battleships. Your course takes you over several enemy paths. As part of your duties, you must lay mines along the enemy’s path. However, in order to plant the mines, you must know the points at which the paths cross and report those points to the Captain and to the Mine Crew. You know of 3 different enemy paths, which are denoted by the following equations:   Enemy Path 1: x – 3y = -15 Enemy Path 2: 4x - y = 7 Enemy Path 3: 2x + y = -1 Your battleship’s course is denoted by this equation: Battleship: x + y = -5 In your tables see if you can be the first group to find the points for where you need to plant your mines!

Solving Systems of Equations in Three Variables (2.2) Now that you are comfortable with system of 2 equations, lets attempt a system of 3 equations!

Solving Systems of Equations in Three Variables (2.2) Solution set is written in an ordered triple: (x, y, z). Remember to check your solution!

Solving Systems of Equations in Three Variables (2.2) Elimination of 3 Variables Steps: Choose two equations and eliminate one variable. Choose two equations again (one must be different) and eliminate the same variable. Using the NEW equations with only two variables from step (1) and (2) eliminate a variable. In step (3) you solved for a variable, substitute what you received for step (3) into one of your two variable equations. In step (3) and (4) you solved for a variable, substitue what you received for step (3) and (4) into one of your original 3 variable equations. Check your solution.

Solving Systems of Equations in Three Variables (2.2) Solution set is written in an ordered triple: (x, y, z). Remember to check your solution!

Solving Systems of Equations in Three Variables (2.2) Substitution of 3 Variables Steps: Best to use if you have one two variable equation. Solve for one of the two variables and substitute your solution into both of your three variable equations. Solve one of your NEW two variable systems for a variable and substitute to solve for the remaining variable in your second NEW equation. Substitute your found variable into one of your two variable equations. Substitute your found variables into one of your three variable equations. Check your solution.

Cool-Down… Do this on Whiteboards! 3-2-1 Processing: List 3 main ideas from todays lesson. List 2 interesting points. List 1 question.