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Section 3-1: Graphing Systems of
Equations
Pages 126-132 in textbook
Objectives
• I can solve systems of equations by graphing
them.
• I can identify the 3 types of solutions to a system
of equations
System of Equations
• When you have 2 or more equations to
solve at one time, we call this a system of
equations.
• The solution set to the system is where the
graphs intersect.
• When will 2 lines intersect? If they have
different slopes.
• Let’s look at an example.
Given the following system of
equations, solve by graphing.
• x + y = 6 and 3x – 4y =4
• One of the easiest ways to graph is to get these
into slope intercept form:
• x + y = 6 becomes
• y = -x + 6
• 3x – 4y = 4
• -4y = -3x + 4
• y = ¾ x -1
yaxis
y=-x+6
9
8
7
6
5
1
(4,2)
0
1
0 -9 -8 -7 -6 -5 -4 -3 -2 -1
4
3
2
0 -1 1 2 3 4 5 6 7 8 9 1
0
-2
-3
-4
-5
y=3/4x -1
-6
-7
-8
-9
xaxis
Calculators
• I want you each to graph these two equations on
your calculators
• y1= -x + 6
• y2 = 3/4x –1
• Graph
• 2nd, Trace, 5(intersect)
• Enter, Enter, Enter
• x=4, y= 2
• (4, 2) (ALWAYS an Ordered Pair)
How about graphs with equal
slopes
• y = 3x –3 and y =3x +3
• The slope is the same in each of these
equations: m=3
• What is the solution?
yaxis
9
8
7
6
5
y=3x+3
4
3
2
1
0
1
0 -9 -8 -7 -6 -5 -4 -3 -2 -1
y=3x-3
0 -1 1 2 3 4 5 6 7 8 9 1
0
-2
-3
-4
-5
No Solution
-6
-7
-8
-9
xaxis
A slightly different example
• What is two equations have the same slope
and same Y-Intercept
• 12x - 9y = 27 and
• 8x – 6y = 18
• Then both will solve to:
• y= 4/3x -3
yaxis
9
8
7
6
5
4
3
2
1
0
1
0 -9 -8 -7 -6 -5 -4 -3 -2 -1
12x-9y=27
0 -1 1 2 3 4 5 6 7 8 9 1
0
-2
-3
8x-6y=18
-4
-5
Infinite solution
-6
-7
-8
-9
xaxis
3 Solution Types
m1  m2
m1  m2
m1  m2
b1  b2
b1  b2
BIG PICTURE
• The solution to a system of equations is where the
graphs cross!
• The solution is always Ordered Pair Format!
• There are 3 types of solutions
– One Solution (Ordered Pair)
– No Solution
– Infinite Solutions
Homework
• WS 4-1