Download presentation

Presentation is loading. Please wait.

Published byChristiana Freer Modified over 2 years ago

1
Systems of Equations Back-Substitution: 3x3 Eliminating one variable Eliminating two variables Copyright © 2011 Lynda Aguirre1

2
Using Back-Substitution An equation can only be solved when there is only one unknown variable Back-substitution steps: 1) Using an equation with only one variable, solve it for that variable Copyright © 2011 Lynda Aguirre2 2) Plug that value into another equation to find a second variable 3) Plug both values into the third equation to find the third variable.

3
Using Back-Substitution An equation can only be solved when there is only one unknown variable Copyright © 2011 Lynda Aguirre3 Back-substitution steps: 1) Using an equation with only one variable, solve it for that variable 2) Plug that value into another equation to find a second variable 3) Plug both values into the third equation to find the third variable.

4
Eliminating a Variable Examine the situation: -This system does not have an equation with only one variable, but it has two equations with 2 variables. We need a preparation step before we can use back-substitution -Then use back-substitution in the original 3x3 system of equations Process: -Using equations 2 and 3, use either substitution or elimination to wipe out one of the variables (y or z). Copyright © 2011 Lynda Aguirre4

5
Eliminating a Variable Examine the situation: -This system does not have an equation with only one variable, but it has two equations with 2 variables. We need a preparation step before we can use back-substitution -Then use back-substitution in the original 3x3 system of equations Process: -Using equations 2 and 3, use either substitution or elimination to wipe out one of the variables (y or z). Copyright © 2011 Lynda Aguirre5

6
Eliminating a Variable Examine the situation: -This system does not have an equation with only one variable, but it has two equations with 2 variables. We need a preparation step before we can use back-substitution -Then use back-substitution in the original 3x3 system of equations Process: -Using equations 2 and 3, use either substitution or elimination to wipe out one of the variables (y or z). Copyright © 2011 Lynda Aguirre6

7
Eliminating a Variable Examine the situation: -This system does not have an equation with only one variable, but it has two equations with 2 variables. We need a preparation step before we can use back-substitution -Then use back-substitution in the original 3x3 system of equations Process: -Using equations 2 and 3, use either substitution or elimination to wipe out one of the variables (y or z). Copyright © 2011 Lynda Aguirre7

8
Eliminating Two Variables Examine the situation: - This system does not have an equation with only one variable, -It also does not have two equations with the same 2 variables. We need several preparation steps before we can use back- substitution We need to create 2 equations with 2 variables by wiping out the third variable. Step 1: First decide whether to wipe out the x’s, y’s or z’s Step 2: Using any two equations, use either substitution or elimination to wipe out the variable you chose. Step 3: Using the third equation and either of the two already used, use substitution or elimination to wipe out the same variable as in step 2. Copyright © 2011 Lynda Aguirre8

9
Eliminating Two Variables Step 3: Using the third equation and either of the two already used, use substitution or elimination to wipe out the same variable (i.e. wipe out the x’s again) Copyright © 2011 Lynda Aguirre9 Step 1: First decide whether to wipe out the x’s, y’s or z’s My choice: Wipe out the x’s Step 2: Using any two equations, use either substitution or elimination to wipe out the variable you chose. My choice: Use equations 1 and 2 and the elimination method to wipe out x’s. We have created one equation with two variables ( y and z) Use equations 1 and 3(since it hasn’t been used yet) and the elimination method to wipe out x’s. We have created another equation with the same two variables ( y and z) Now take these two new equations (in two variables) and eliminate another variable

10
Copyright © 2011 Lynda Aguirre10 Eliminating Two Variables Step 4: Now use these two equations and either substitution or elimination to wipe out one of the remaining variables (y or z). My choice: Use the elimination method to wipe out the z’s. Now do back-substitution into either one of the equations above

11
Copyright © 2011 Lynda Aguirre11 Eliminating Two Variables My choice: Plug y=1 into the top equation to find z. Now do back-substitution into any of the original three equations (with y=1 and z=2) ORIGINAL 3 EQUATIONS My choice: Plug y=1 and z=2 into the top equation to find x.

Similar presentations

OK

Lesson 4-2: Solving Systems – Substitution & Linear Combinations Objectives: Students will: Solve systems of equations using substitution and linear combinations.

Lesson 4-2: Solving Systems – Substitution & Linear Combinations Objectives: Students will: Solve systems of equations using substitution and linear combinations.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on banking sector in pakistan Ppt on asia the continent of contrast Ppt on save environment image Product mix ppt on nestle promotion Ppt on hplc method development and validation Ppt on fire extinguisher types pictures Ppt on classical economics theory Ppt on content development exercises Insect anatomy and physiology ppt on cells Muscular system anatomy and physiology ppt on cells