Linear Equations -- Review.

There isn't very many parts to this unit.. but it was still a lot to learn and take in.
The following is all what I have learned in the last couple weeks:
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• SYSTEM - Two or more equations that exist in the same plane
• Here is what you can do with two lines in the same plane, there is 3 ways.

1.Parrellel

2. Intersecting

3. Superimposed

I couldnt find a picture that represented this one very well, but; it is when the lines are on top of eachother.

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There are 2 solving methods;

• Substitution
• Elimination

Substitution - -

Step 1. Choose a variable in either equation to be solved for.

Step 2. Solve for it.

Step 3. Substitute so that you create a single equation in one variable.

Step4. Solve for that variable we get.

Step5. Use that known value to solve for the unknown value. By substituting into either original equation.

I was looking around the internet and I found this, so i copied it and pasted it onto here. Take a look, its a simple question but it shows how to do it.

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Elimination Method

Step1. Line up variables and coefficients.

Step 2. Pick a variable, depends on each case. (Pick which ever is easier)

Step 3. Use algebra to multiply and divide an entire equation by a valve to create SAME OR OPPOSITE coefficients in either variable.

Step 4. ADD OR SUBTRACT depending on wether you've created SAMES(subtract) OR OPPOSITES(add)

Step 5. SOLVE for the remaining variable, use substitution to find first variable, (once again in either question.)

Example:)

LOOK AT IT. VERY SIMPLE.

http://rachel5nj.tripod.com/NOTC/ssoewog2.html

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Types of Solutions

1. Ordered Pair solution - Consistent system(lines intersect); Slopes, different; Intercepts, Diff unless intersection is on that intersect.
2. No Solution - Inconsistent system(lines are parallel); Slope,SAME; Intercepts, DIFF;
3. Infinitely many ordered solutions - Dependant system; (lines are superimposed); Slope,SAME; Intercept, DIFF;.

Example.

Line 1. 5x-3y=4

Line 2. 7x - 3y=4

How many solutions? ONE.

As soon as the slopes are different, there is only one solution.

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Out of everything we learned, I noticed that the Elimination method was easiest. Substitution took a lot of time to get used to, It was hard in the beginning, but now that I make myself go throughly through the steps, its a lot easier.

The word problems tended to create a lot of problems. I got to the Let statements, but hardly ever passed that. The joke sheet did help, but not sure how well I know how to do them yet. This test should help a lot and show me what I could and should try harder on.

Those were my notes on what I learned, hope they helped at least a little bit. The others who have posted, They helped me alot, even creating my cheat sheet thing, it helped.