So on Friday's class we learnt a few things . . .

To start off we look at the three types of systems (Shown on page 13 in the book)

1) Consistent and Independent Systems

2) Inconsistent and Dependent Systems

3) Consistent and Dependent Systems
We first looked at number one, Consistent and Independent Systems. Mr. P explained how 2x + 3y = 5 & 4x + y = -2 would not be good to look at first strictly for illustrated purposes and then decided to change them to x - y - 1 = 0 & 2x + y = -4
x - y - 1 = 0      2x + y = -4

 y = x - 1            y = -2x - 4 

 x  | y                  x | y 

-2 | -3               -2 |  0

-1 | -2               -1 | -2

0 | -1                  0 | -4

1 |  0                  1 | -6

2 | 1                                                                           

Step one .
- Make a table of values  

Step two.
- Plot the points

Step three.
- Observe the values
* Clearly see this graph is Consistent and Independent *

Step four.
- Fill in the graph shown underneath the graph .

                                        

 [ C H A R T ]
 lines meet at ( -1, -2 )         <-- This is the solutions
 lines have different slopes  lines have different y-intercepts

Next we looked at Consistent and Dependent, we did the table of values for the first; plotted that .
Then converted 2x + 2y = 2 -- > 2y = -2x + 2 -- >  y = -x + 1 and found that they were the same line .

 [ C H A R T ]
the lines have the same slopesthe lines have the same y-intercepts they are the same line 
* every point along the line is considered a solution







Last we look at Inconsistent Systems we once again changed the original equations to make it easier although Mr. P said you are welcome to do the originals so that you can have more practice (:

[ C H A R T ]
Lines have the same slope                        
The lines have different y- intercepts          
The lines are parallel and have no solutions

Next Mr. P explained that the chart located on page 17 summarizes what we learned in class on Friday ...

                                      Consistent                               Inconsistent
                           Independent     Dependent    

type of line  -- > different line       same line                      parallel

solutions -- >     one solution       infinate solution           no solution

slopes -- >        different slope   same slope


We then moved on to page 18 to look at "solving systems of linear equations two equations two unknowns"

We finished this assignment in class and then a few people put the solutions on the smart for for Sarah ( Hi Sarah hope you are having a great time ! ) Mr. P handed out another work book and that was the end of the class ...
Hope you had a good weekend ! See you in class tomorrow morning (: