6.1 Solving Systems Of
Equations By Graphing
Bell Work
Evaluate each expression for x = 1 and y = –3.
1. x – 4y
2. –2x + y
Write each expression in slope-intercept form.
3. y – x = 1
4. 2x + 3y = 6
5.
Cheetah Vs. Usain Bolt
Video: http://youtu.be/U6K-F9Bjl8s
D
i
s
t
a
n
c
e
100 m
(5.95, 100)
Bolt=
(9.58, 100)
Cheetah
=
Time
9 10
D
i
s
t
a
n
c
e
Bolt=
100 m
(9.58, 100)
Cheetah
=
40 m
Time
9 10
Solving Linear Equations By
Graphing
• Our goal is to;
1. Graph TWO lines on same graph
2. Locate where they intersect (or if
they do at all)
Solving a Linear Equation
• Linear equations can look like;
y = 3x + 7
Or
-3x + y = 7
Or
7 + 3x = y
Or
…
3 Graphing Possibilities
1. Intersecting Lines
2. Parallel Lines
3. Coinciding Lines
1) Intersecting Lines
• The point where the
lines intersect is your
solution.
• The solution of this
graph is (1, 2)
(1,2)
What is the solution of the system
graphed below?
1.
2.
3.
4.
(2, -2)
(-2, 2)
No solution
Infinitely many solutions
Where do these graphs intersect
2) Parallel Lines
• These lines never
intersect!
• Since the lines never
cross, there is
NO SOLUTION!
• Parallel lines = SAME
SLOPE, different y-int.
2
Slope = = 2
1
y-intercept = 2
y-intercept = -1
Parallel Lines
Hi, I’m Two
Our Slopes Must
Be Twins!!!
Hey, I’m Two
Too!
What is the solution of this system?
y = 3x + 3
y = 3x - 12
1.
2.
3.
4.
(3, -12)
Parallel solutions
No solution
Infinitely many
solutions
3) Coinciding Lines
• These lines are the
same!
• Since the lines are on
top of each other, there
are
INFINITELY MANY
SOLUTIONS!
• Coinciding lines = SAME
SLOPE, SAME Y-INT.
2
Slope = = 2
1
y-intercept = -1
What is the solution of this system?
y = 3x - 8
y = 3x - 8
1.
2.
3.
4.
(3, 1)
(4, 4)
No solution
Infinitely many
solutions
Lets try one: Find the solution to the
following system:
y = -2x+4
y = x -2
m=-2
b=4
m=1 b=-2
Step 1:Graph both equations
Step 2: Find
Where the lines intersect?
THE SOLUTION:
(2,0)
You try: Where do the lines
intersect?
y = 2x – 1
y = –x + 5
Graph both
equations
Where do they
intersect?
The point
is (2, 3)
Try again: Find the solution to
the system
 Graph
both
equations
Where do they
intersect?
NO SOLUTION
Find the Solution
Summary
• Intersecting Lines have how many
solutions?
• Parallel Lines have the same what?
• How can you tell if two equations are
coinciding without graphing them?
• Do you have to graph the system to
know the answer if both equations
have the same slope?
HOMEWORK
• Find an example in real life (just like
Usain Bolt vs. Cheetah) and graph it.
– I want to see the following
1.
2.
3.
4.
What two things are you graphing
What is your x-axis and y-axis
Graph them
Do they intersect? Where?