This document provides instructions and examples for solving systems of linear equations without graphing. It explains that by setting the two equations equal to each other, one can isolate a variable and substitute it back into one of the original equations to find the solution. Sample problems are worked through step-by-step, showing how to eliminate variables through addition or multiplication to discover the point where the lines intersect. The key steps of setting the equations equal, eliminating a variable, and back-substituting are demonstrated.

1. Skill 28 A System of Two Equations Page 142 in the book
This lesson is about an algebraic way to figure out where two lines (think y = mx + b)
will intersect on the number plane. By using algebra, we don’t have to graph.
Here is a picture (graph) of what we will find out without graphing.
We have two lines and are looking for the ordered pair (x,y) where they
meet on the number plane. These lines meet at (1,2) or x = 1 and y = 2.
Instead of graphing and reading the point off the graph, we will figure this out
by using algebra. See the next slide.

2. Page 143 has a detailed set of examples from a puzzle Page 144 in our book but
Referenced by the puzzle page 164. I did this typed page before I put your book together.
After looking at my examples here, go back and look at page 143.
Here is the problem we will do together.
Notice that the equations are in
Standard form. Ax + By = C
This means the x and y are on the same side
of the equation and the number is on the
other side.
Now that we know y = -1,
go to either of the original
equations, and substitute
-1 for y.
In the first equation, this would
look like:
2x + (-1) = 3 or
2x -1 = 3 Add 1 to both sides
2x = 4 Divide by 2 and
X = 2 Solution (2, -1)

3. There are times when word problems can be solved much more easily when
you can use two variables (x and y). Some examples are like page 145
I set up all the word problems on page 146. Here is number 1. Notice how we
can solve it.
___________________________
2x = 108
Divide by 2 to get x = 54.
So, then replace x with 54 in
equation 1 and we get y as 36.
The two numbers are 54 and 36.

4. Do Not worry about the word problems. Just try to get the problems like
Page 144, 1-8 mastered. That will be enough to get the GED question right I think.

5. Problem 3
The idea is to
Eliminate x or y.
By just adding
as the equations
are, we can
Eliminate y.
So, x = -5.
Find y by replacing
X with -5 in either
of the original
Equations.
In the first equation we can say, 3(-5) + 5y = 0
-15 + 5y = 0
+15 +15
5y = 15
y = 3
So, the values x = -5 and y = 3 make both equations true.
The point of intersection if we graphed the two lines is (-5, 3).

6. Now look at the problem from page 147 problem A.
Notice that if we just add, we do not eliminate either x nor y.
This might happen on the test; however, it may not. Just in case, here is how to think about it.
If there was a 2 in
Front of the y in
Equation 2, we would
Be able to add.
So, if we multiply
All the terms in
Equation 2 by 2,
It will now look like
This.

7. Now in either equation 1 or 2 (original ones), let x = 2 and find y.
In original equation 2, we have 3(2) + y = 9
6 + y = 9
-6 -6
y = 3
So the solution is x = 2 and y = 3 or just the ordered pair (2,3).