Welcome to September! Please do the following: 1)Pick up an assignment list and Entry Ticket 2)Begin your Entry Ticket Homework: o HW Pg. 71 #11-31 odd (15, 17, 19 use graphing calculator), 32; Pg. 76 #9-15 odd Updates:1 Question Graphing Calculator Quiz 2.1 1/5 periods on 9/4 6 period on 9/5

Agenda 1)Entry Ticket 2)Unit 1 Test 3)U2L1 4)Wartime Battle 5)U2L1 Continued… 6)Cool-Down…

Entry Ticket

Unit 1 Test A: B: C: Below a 35, please come see me during tutorial

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

Solving Systems of Equations in Two Variables (2.1) System of Equations o A set of two or more equations. o To solve a system of equations means to find values for the variables in the equations which make all the equations true. o 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). o 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)

Now let’s write the more academic names for these lines!

Steps for Graphing on a Calculator 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: ①Press y = ②Type in your equation 3x + 2 ③Press Zoom ④Since 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: ①Press y = ②Type in your equation 3x + 50 ③Press Zoom ④Since 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. ⑤Usually on a graph we want to see the x and y-axis. You must play with the window. Press Window. ⑥Adjust 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.

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!

Paths Enemy Path 1 Enemy Path 3 Enemy Path 2Mine # 1,( -7.5, 2.5) Mine # 2,( 0.5, -5.5) Mine # 3,( 4,-9)

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: ①Choose two equations and eliminate one variable. ②Choose two equations again (one must be different) and eliminate the same variable. ③Using the NEW equations with only two variables from step (1) and (2) eliminate a variable. ④In step (3) you solved for a variable, substitute what you received for step (3) into one of your two variable equations. ⑤In 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. ⑥Check 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. ①Solve for one of the two variables and substitute your solution into both of your three variable equations. ②Solve one of your NEW two variable systems for a variable and substitute to solve for the remaining variable in your second NEW equation. ③Substitute your found variable into one of your two variable equations. ④Substitute your found variables into one of your three variable equations. ⑤Check your solution. Solving Systems of Equations in Three Variables (2.2)

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