systems of equations back-substitution: 3x3 eliminating one variable eliminating two variables...

Systems of Equations

Back-Substitution: 3x3

Eliminating one variable

Eliminating two variables

Copyright © 2011 Lynda Aguirre 1

Using Back-SubstitutionUsing Back-SubstitutionAn 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


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.

Using Back-SubstitutionUsing Back-SubstitutionAn 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 variable2) Plug that value into another equation to find a second variable3) Plug both values into the third equation to find the third variable.

Eliminating a VariableEliminating 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).


Eliminating Two VariablesEliminating 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’sStep 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.



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)


Step 1: First decide whether to wipe out the

x’s, y’s or z’sMy 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

Now take these two new equations (in two variables) and eliminate another

variable



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



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.

systems of equations back-substitution: 3x3 eliminating one variable eliminating two variables...

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