Math 1 Chapter 7 Notes.notebook January 11, 2016

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1 Chapter 7 Things you must know 1

2 Math 1 Chapter 7 Notes.notebook 2

3 Math 1 Lesson 7-1 Date: Title: Solving linear systems by graphing pg. 427 Key Vocab: System of linear equations: also called a linear system, consists of two or more linear equations in the same variable. Example: Solution of a system of linear equations: in two variables is an ordered pair (a point) where the two lines cross. Consistent independent system: A linear system that has exactly one solution Example 1: use the graph to solve the system then check algebraically Example 2 solve the linear system When solving systems of equations 3 things can happen pg odd pg.431 9, 13,18,23 3

4 Math 1 Lesson 7-2 Date: Title: Solving linear systems by substitution pg. 435 Next year teach first Steps to follow for solving a system by substitution CHUNKING 1. Get one of the variables by itself in one of the equations 2. Substitute the expression in step one into the other equation. In other words you are taking two equations and writing it as one equation 3. Solve for the variable either x or y 4. Plug that value in for one of the equations and then find the other variable Example 1 Solve by substitution remember each answer is a point (x,y) Example 3 pg odd 25. 4

5 Math 1 Lesson 7-3 Date: Title: Solving linear systems by ELIMINATION pg. 444 Steps to follow when using elimination When both equations are in standard form is when you want to use elimination 1. First create opposites with either the x or y coefficients 2. Add the two equations together... Remember you can only add x's to x's, y's to y's and #s to #s 3. Solve for the one variable 4. substitute the value in for the variable and solve for the other variable. REMEMBER the solution is a point (x,y) Example 1,2 and 3: Solve the linear system pg ,9,17,21,35 pg odd 27. 5

6 Math 1 Chapter 7 Notes.notebook Date: Math 1 Lesson 7-4 Title: Solve linear systems by multiplying first pg.451 Opposites: 2x and -2x -3y and 3y Equivalent equations Equivalent SYSTEMS Steps to follow when using elimination When both equations are in standard form is when you want to use elimination 1. First create opposites with either the x or y coefficients 2. Add the two equations together... Remember you can only add x's to x's, y's to y's and #s to #s 3. Solve for the one variable 4. substitute the value in for the variable and solve for the other variable. REMEMBER the solution is a point (x,y) example 1 and 2 Rules to live by when solving systems of equations There are 4 ways to solve a system of linear equations 1. Graphing: Use this method when the graphs are EASY to graph and you have graph paper available 2. Substitution: Use this method when one of the variables are by itself ALREADY or it can be done easily. 3. Elimination (opposites) : Use when both equations, are in standard form. 4. Solve by matrices but I will teach you this later pg odd 1-11 odd 6

7 7

8 SUMMARY for graphing absolute Values Grandparent function Parent function a tells you if the absolute value opens up or down and is wide or narrow h translates the graph left if there is a + in front of the h and right if there is a - sign infront of the h right 4 left 2 k translates the parent function up if there is a + sign in front of the k and down if there is a - sign in front of k up 3 down 5 8

9 Math 1 Lesson 7-5 Date: Title: Solve special types of linear systems pg.459 When solving systems of equations 3 things can happen one solution Infinitely many No solutions solutions Consistent INDEPENDENT System x=# y=# (x,y) Different SLOPES Consistent DEPENDENT System TRUE STATEMENT 6=6 Same slopes Same intercepts Inconsistent system FALSE STATEMENT 5=12 Same slopes different intercepts Example 1 and 2 find the solutions to the system Example 3: WITHOUT solving the system, tell whether the linear system has one solution, no solutions or infinitely many solutions pg odd #37 9

10 Math 1 Chapter 7 Notes.notebook Math 1 Lesson 7-6 Date: Title: Solving systems of linear inequalities pg.466 Graph the linear inequality REMEMBER 6-7 Key vocab: System of linear inequalities: Consists of two or more linear inequalities in the same variables Solution of a system of linear inequalities: ordered pairs (points) that are solutions to each inequality in the system Example 1 and 2 Graph the system in inequalities Example 3 WRITE a system of inequalities for the shaded region wksh

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14 Attachments Book Copy of ML Alg 1 Pacing.xlsx 7 6 wksh Alg 1.pdf

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1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =

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