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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 )
LINEAR SYSTEMS – Graphing Method
Example # 1 : Find the intersection point of the following system of
equations :
32
244
yx
yx
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
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
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
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
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
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
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 )
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
LINEAR SYSTEMS – Graphing Method
Example # 2 : Find the intersection point of the following system of
equations :
1
63
2
xy
xy
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
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
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
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
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
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
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
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
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 )
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
LINEAR SYSTEMS – Graphing Method
Example # 3 : Find the intersection point of the following system of
equations :
73
52
xy
xy
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 :
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 :
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 :
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 :
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 :
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 :
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 :
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
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 )
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
