![Page 1: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/1.jpg)
LINEAR SYSTEMS – Graphing Method
In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect.
You can use either an ( x , y ) table, or slope – intercept to graph your lines.
INTERSECTION POINT
( x , y )
![Page 2: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/2.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
![Page 3: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/3.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
Using an ( x , y ) table :
x y x y
244 yx 32 yx
![Page 4: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/4.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
Using an ( x , y ) table :
x y
0 6
x y
6
244
2440
244
y
y
y
yx244 yx 32 yx
![Page 5: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/5.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
Using an ( x , y ) table :
x y
0 6
4 5
x y
5
204
2444
244
y
y
y
yx244 yx 32 yx
![Page 6: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/6.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
Using an ( x , y ) table :
x y
0 6
4 5
x y
5
204
2444
244
y
y
y
yx244 yx 32 yx
![Page 7: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/7.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
Using an ( x , y ) table :
x y
0 6
4 5
x y
0 - 3
3
30
302
32
y
y
y
yx244 yx 32 yx
![Page 8: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/8.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
Using an ( x , y ) table :
x y
0 6
4 5
x y
0 - 3
1 - 1
1
32
312
32
y
y
y
yx244 yx 32 yx
![Page 9: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/9.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
Using an ( x , y ) table :
x y
0 6
4 5
x y
0 - 3
1 - 1
244 yx 32 yxINTERSECTION POINT
( 4 , 5 )
![Page 10: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/10.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
Using an ( x , y ) table :
2424
24204
24544
244
yx
33
358
3542
32
yx
INTERSECTION POINT
( 4 , 5 )
CHECK CHECK
![Page 11: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/11.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
![Page 12: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/12.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
x y
63
2 xy
x y
1 xy
![Page 13: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/13.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
x y
0
63
2 xy
x y
1 xy
603
2y
![Page 14: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/14.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
x y
0 6
63
2 xy
x y
1 xy
6
60
603
2
y
y
y
![Page 15: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/15.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
x y
0 6
3 8
63
2 xy
x y
1 xy
8
62
633
2
y
y
y
![Page 16: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/16.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
x y
0 6
3 8
63
2 xy
x y
1 xy
8
62
633
2
y
y
y
![Page 17: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/17.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
x y
0 6
3 8
63
2 xy
x y
0 1
1 xy
1
10
1
y
y
xy
![Page 18: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/18.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
x y
0 6
3 8
63
2 xy
x y
0 1
1 0
1 xy
0
11
11
y
y
y
![Page 19: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/19.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
x y
0 6
3 8
63
2 xy
x y
0 1
1 0
1 xy
0
11
11
y
y
y
![Page 20: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/20.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
x y
0 6
3 8
63
2 xy
x y
0 1
1 0
1 xy
INTERSECTION POINT
( – 3 , 4 )
![Page 21: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/21.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
Using an ( x , y ) table :
44
624
633
24
63
2
xy
44
134
134
1
xy
INTERSECTION POINT
( – 3 , 4 )
CHECK
CHECK
![Page 22: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/22.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 3 : Find the intersection point of the following system of
equations :
73
52
xy
xy
![Page 23: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/23.jpg)
LINEAR SYSTEMS – Graphing Method
73
52
xy
xy
I will use slope – intercept on this one…
52 xy
51
2
b
m
Example # 3 : Find the intersection point of the following system of
equations :
![Page 24: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/24.jpg)
LINEAR SYSTEMS – Graphing Method
73
52
xy
xy
I will use slope – intercept on this one…
52 xy
51
2
b
m
Example # 3 : Find the intersection point of the following system of
equations :
![Page 25: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/25.jpg)
LINEAR SYSTEMS – Graphing Method
73
52
xy
xy
I will use slope – intercept on this one…
52 xy
51
2
b
m
Example # 3 : Find the intersection point of the following system of
equations :
![Page 26: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/26.jpg)
LINEAR SYSTEMS – Graphing Method
73
52
xy
xy
I will use slope – intercept on this one…
52 xy
51
2
b
m
Example # 3 : Find the intersection point of the following system of
equations :
![Page 27: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/27.jpg)
LINEAR SYSTEMS – Graphing Method
73
52
xy
xy
I will use slope – intercept on this one…
52 xy
51
2
b
m
73 xy
71
3
b
m
Example # 3 : Find the intersection point of the following system of
equations :
![Page 28: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/28.jpg)
LINEAR SYSTEMS – Graphing Method
73
52
xy
xy
I will use slope – intercept on this one…
52 xy
51
2
b
m
73 xy
71
3
b
m
Example # 3 : Find the intersection point of the following system of
equations :
![Page 29: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/29.jpg)
LINEAR SYSTEMS – Graphing Method
73
52
xy
xy
I will use slope – intercept on this one…
52 xy
51
2
b
m
73 xy
71
3
b
m
Example # 3 : Find the intersection point of the following system of
equations :
![Page 30: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/30.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 3 : Find the intersection point of the following system of
equations :
73
52
xy
xy
I will use slope – intercept on this one…
52 xy
51
2
b
m
73 xy
71
3
b
m
![Page 31: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/31.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 3 : Find the intersection point of the following system of
equations :
73
52
xy
xy
I will use slope – intercept on this one…
52 xy
51
2
b
m
73 xy
71
3
b
m
INTERSECTION POINT
( 2 , – 1 )
![Page 32: LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You](https://reader035.vdocument.in/reader035/viewer/2022062802/56649ee15503460f94bf1bb7/html5/thumbnails/32.jpg)
LINEAR SYSTEMS – Graphing Method
Example # 3 : Find the intersection point of the following system of
equations :
73
52
xy
xy
I will use slope – intercept on this one…
11
541
5221
52
xy
11
761
7231
73
xy
INTERSECTION POINT
( 2 , – 1 )
CHECK CHECK