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Lesson Systems Graphing
There are several ways to solve a  system of equations
There are several ways to solve a  system of equations
Graphing
There are several ways to solve a  system of equations
Graphing
Substitution
There are several ways to solve a  system of equations
Graphing
Substitution
Elimination
There are several ways to solve a  system of equations
This lesson will be dealing with graphing
Graphing
Substitution
Elimination
If I am given a system of equations
If I am given a system of equations
x - y = 2
x + y = 8
If I am given a system of equations
I can use a graph to solve
x - y = 2
x + y = 8
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

x
y
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

x
y
1 + y = 8
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

x
y
-1
1 + y = 8
-1
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

x
y
-1
1 + y = 8
y = 7
-1
Fill in the y value
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

x
7
y
-1
1 + y = 8
y = 7
-1
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

2
x
7
y
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

2
x
7
y
2 + y = 8
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

2
x
7
6
y
-2
2 + y = 8
y = 6
-2
Fill in the y value
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

2
x
7
6
y
Graph (1 , 7)
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

2
x
7
6
y
Graph (1 , 7)
(1 , 7)
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

2
x
7
6
y
graph (2 , 6)
then
Fill in the y value
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

2
x
7
6
y
graph (2 , 6)
then
(2 , 6)
4
-4
8
-8
4
-4
8
-8
12
-12
First I graph x + y = 8
x - y = 2
x + y = 8

1

2
x
7
6
y
then draw
the line
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

x
y
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

x
y
1 - y = 2
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

x
y
-1
1 - y = 2
-1
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

x
y
-1
1 - y = 2
- 1y = 1
-1
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

x
-1
y
-1
1 - y = 2
- 1y = 1
y = -1
-1
Solve for y
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

2
x
-1
y
2 - y = 2
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

2
x
-1
y
-2
2 - y = 2
-2
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

2
x
-1
y
-2
2 - y = 2
- y = 0
-2
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

2
x
-1
0
y
-2
2 - y = 2
- y = 0
y = 0
-2
Solve for y
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

2
x
-1
0
y
Graph (1 , -1)
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

2
x
-1
0
y
Graph (1 , -1)

( 1 , -1)

4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

2
x
-1
0
y
Graph (2 , 0)
Give the y value
(2 , 0)
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
Now graph x - y = 2

1

2
x
-1
0
y
then draw
the line
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
The intersection is the
answer
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
The intersection is the
answer
Intersection
(5 , 3)
Point
4
-4
8
-8
4
-4
8
-8
12
-12
x - y = 2
x + y = 8
The intersection is the
y = 3
x = 5
answer

Give the y value

Intersection
(5 , 3)
Point
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