Test Review

Definition of Linear Equations: Two or more equations that exist in the same plane constitute a system... All equations are linear. This is basically what we've been working on for the past few weeks.
Just a quick recall from last year:
slope and y-intercept...... y=mx+b
standard form...... Ax+By+C=0
y-y1=m(x-x1)
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Than from there, we were taught the Substitution Method, in a variety of different steps
Step 1) choose a variable in either question to be "solved for"
Step 2) solve for the variable
Step 3) substitute so that you can create a single equation in one variable
Step 4) solve for that variable
Step 5) use that known value to solve for the unknown value by substituting into either original equation

Algebraic Solving Method #2: Elimination Method/ Addition and Subtraction Method/ Linear Combination Method.
Step 1) line up variables and coefficients
Step 2) pick a variable to solve for
Step 3) use algebra to multiply/ divide an entire equation by a value to create the SAME OR OPPOSITE COEFFICIENTS in either variable
Step 4) Add or subtract depending on whether you created sames or opposites... for same you subract, for opposite you add
Step 5) solve for remaining variable
Step 6) use substitution

I'm pretty comfortable using both the elimination method and the substitution method. More so the elimination method, because when sometimes when I do the substitution method, I confuse myself in what variable I should solve for first.

Now for what I find most challenging..... Word Problem Strategies.
Step 1) LET STATEMENTS..
Step 2) the two equations in two variables each
Step 3) Do the math! either elimination method, graphing calculator, graphmatika, etc..
Step 4) create a sentence summarizing your answer

Word Problems to me, are terrible. When we do them as a class, they are easy, but when i take them home and trying to find the let statements is very difficult. These will be something that i'll study tonight.

The different types of solutions to Linear Equations:
1) Ordered Pairs Solution..
Consistent System (lines intersect)
Slopes: different
Intersect: different

2) No solution
Inconsistent System (lines parallel)
Slopes: same
Intersect: all different

3) Infinetly many ordered pair solutions
Dependant System (lines are super imposed)
slope: Same
intersect: Same

Anyway.... So these are a quick summary of all the notes that I've taken in class. In my opinion, this unit wasn't too difficult, but decently challenging. But I need to work on how to understand and set up the equations in the word problems.