Solving a System of Linear Equations

HEY! I'll just cut through the intro and get this scribe started.

On Friday's class we sort of started something new, but we still used some previous knowledge in order to work with the following questions.

We were given two equations.

x + y = 6
x - y = 2

y = -x + 6
x - 2 = y

Question: Do the lines intersect?
_________ Where?

It's better to know more than one way to solve a problem. You have to take on a certain equation in as many different angles as you can.

Mr. K taught us different ways to solve the equation.

There were 4 different techniques that he showed the class.

1. Graph : to actually draw out the equation on a graph
   
2. Comparison
   
3. Substitution
   
4. Elimination

*Important note: The Lattice Point is a point in the cartesian plane where the points are integers. (where the lines cross)

GRAPH

We've graphed the lines and can easily see where the lines cross (4,2). Graphing it will not always solve the problem because the point where the lines intersect won't always be a Lattice point.

COMPARING

At the Intersection, Y1 & Y2 are the same.

eg.)

y = -x + 6
x - 2 = y

-x + 6 = x - 2
____8 = 2x
____4 = x

This technique is called comparison. It's when 2 things equal to the same thing.


SUBSTITUTION


To figure out the rest, substitute 4 for x.

x + 4 = 6
4 + y = 6
y = 2

Lines intersect at (4,2)

ELIMINATION



OK...hopefully people will be able to understand this..

The Homework is Exercise 24

Next Scribe is: M@rk