Chapter 1 Summary---

There are two techniques--
· Solve by Elimination, which is the adding or subtracting technique to eliminate the variables.
Example:  -3x+5y=11
      7x-5y=14
Multiply each equation to get the same.
     -21x+30y=77
     -25x+30y=70
Add/ Subtract to get x or y.
     -21x+30y=77
    - -25x+30y=70
     4x/(4) =7 /(4)
       x= 7/4
Substitute to get the y value.
And Since -->   3(1.75)+5y=11
        5.25-5.25 +5y=16.25-5.25
        5y/(5)=16.25 /(5)
So y now equals  y=3.25
So -->      (7/4, 13/4)

·Solve by Substitution, which is substituting the variables to get the answer in the end.
Step 1: Choose a variable in either equation to be solved for.
Step 2: Solve for that variable.
Step 3: Substitute so you can create a single equation in 1 variable.
Step 4: Use that known value to solve for the unknown by substituting the variable with the answer from before.
You will then get the coordinates for both the equations combined.
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Types of Solutions
Ordered Pair solution - Consistent system (lines intersect). The slopes are different; the intercepts are different, unless there is an intersection with the two lines.
No Solution - Inconsistent system (lines are parallel). The slopes are the same, the intercepts are different.
Infinitely many ordered solutions - Dependant system (lines are superimposed). The slopes are the same, the intercepts are different.

That was an example of what I knew how to do. I understood the elimination and substitution methods without any problems. I had a problem with the 4- Step Word Problem solving. I understood the Let a or b equal part. I just didn’t understand how to solve after that. I still have problems with these types of questions, but other than that.. It's all good:)