W1D2 ­ Algebraically Solving Linear Systems.notebook

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January 30, 2013

January 30th

Aim:

Due Next Class: 

Get Ready:

Algebraically Solving Linear Systems

 HW 2

Quiz on Thursday

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How can we represent Superman's powers in terms of Spiderman's??

W1D2 ­ Algebraically Solving Linear Systems.notebook

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January 30, 2013

Solving a system using Substitution!

Using what you know is true about one variable to replace the other variable. 

For example, we replaced the Batman variable

Lonely Variable: a variable by itself on one side of the equals sign

y = 3x + 2 

W1D2 ­ Algebraically Solving Linear Systems.notebook

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January 30, 2013

Example 1:

2x + 3y = 6  

y = 3x + 2 

Steps to Solving using Substitution

1. Isolate the lonely variable if it isn't alone already.

2. Substitute your equation from the first step into the OTHER equation in the system.

3. Simplify to solve for one of the variables.

4. Plug your solution from step 3 into the original equation to solve for the lonely variable.

5. Write out the solutions to both variables.

W1D2 ­ Algebraically Solving Linear Systems.notebook

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January 30, 2013

Example 2:

­a + b = ­2 

­3a + 2b = ­ 6

Steps to Solving using Substitution

1. Isolate the lonely variable if it isn't alone already.

2. Substitute your equation from the first step into the OTHER equation in the system.

3. Simplify to solve for one of the variables.

4. Plug your solution from step 3 into the original equation to solve for the lonely variable.

5. Write out the solutions to both variables.

*first look for any variables without coefficients!!

W1D2 ­ Algebraically Solving Linear Systems.notebook

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January 30, 2013

Example 3:

2w + 2z = 4 

­4w­ 3z = 8 

Steps to Solving using Substitution

1. Isolate the lonely variable if it isn't alone already.

2. Substitute your equation from the first step into the OTHER equation in the system.

3. Simplify to solve for one of the variables.

4. Plug your solution from step 3 into the original equation to solve for the lonely variable.

5. Write out the solutions to both variables.

*first look for any variables without coefficients!!**then look for any equations with a GCF

W1D2 ­ Algebraically Solving Linear Systems.notebook

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January 30, 2013

Example 4:

2k ­ 3j = ­1 

j = 3 

Steps to Solving using Substitution

1. Isolate the lonely variable if it isn't alone already.

2. Substitute your equation from the first step into the OTHER equation in the system.

3. Simplify to solve for one of the variables.

4. Plug your solution from step 3 into the original equation to solve for the lonely variable.

5. Write out the solutions to both variables.

W1D2 ­ Algebraically Solving Linear Systems.notebook

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January 30, 2013

Practice

W1D2 ­ Algebraically Solving Linear Systems.notebook

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January 30, 2013

SYSTEMS of EQUATIONS

A system of equations is a collection of two or more equations with a same set of unknowns. 

In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. 

what do we do with them? how are they useful? how can we solve them?

W1D2 ­ Algebraically Solving Linear Systems.notebook

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January 30, 2013

Recap

Next Class:  Due Next Time:

Key Points

1) How do we know if a point is the solution to a system of linear equations?

2) Can we ever have two points as the solution?