How many
solutions to
the system
of equations?
Copyright 2012
Jamie Riggs http://missmathdork.blogspot.com/
How Many Solutions to the system?
Method
One Solution
No Solutions
Infinite Solutions
Graphing
Best to use when:
Both equations are
in slope intercept
form:
Augmented Matrices
y=mx+b
Best to use when:
Substitution
intersection of the lines.
Lines are parallel and do
not intersect.
Lines are identical and
intersect at every point
Answer matrix will
Answer matrix will
Answer matrix will
1 0 # 
0 1 # 


1 # # 
0 0 1 


1 # # 
0 0 0 


After substituting
After subsituting,
take the form:
Both equations are
in standard form:
Ax + By = C
Best to use when:
take the form:
take the form:
After substituting and
simplifying you will be left
with
One equation has
variables will form zero
variables will form zero
with a TRUE equation
been solved for a
x=#
y=#
with a FALSE equation
y=-x+1
Solution will take the
2=3
3=3
Best to use when:
After eliminating and
After eliminating,
After eliminating,
variable.
2x + 3y = 2
Coefficients of
Elimination
Solution is the point of
form of (x, y)
simplifying you will be left
with
variables are
variables will form zero
y=#
with a FALSE equation
with a TRUE equation
Solution will take the
0=3
x=#
easily made opposites
3x+ 4y = 7
pairs and will leave you
variables will form zero
opposites or can be
using multiplication.
pairs and will leave you
-3x + 7y = 4
Copyright 2012
form of (x, y)
pairs and will leave you
pairs and will leave you
Jamie Riggs http://missmathdork.blogspot.com/
0=0
How Many Solutions to the system?
Method
One Solution
No Solutions
Infinite Solutions
Graphing
Best to use when:
Both equations are in
slope intercept form:
y=mx+b
Substitution
Best to use when:
Solution is the point of
intersection of the lines.
Lines are parallel and do
not intersect.
Lines are identical and
intersect at every point
After substituting and
simplifying you will be
left with
One equation has
been solved for a
x=#
variable.
y=#
y=-x+1
Solution will take the
2x + 3y = 2
After substituting
After subsituting,
variables will form zero
variables will form zero
with a FALSE equation
with a TRUE equation
pairs and will leave you
pairs and will leave you
2=3
3=3
After eliminating,
After eliminating,
form of (x, y)
Best to use when:
Coefficients of
variables are opposites
3x+ 4y = 7
After eliminating and
Elimination
-3x + 7y = 4
or can be easily made
opposites using
multiplication on one
-2(3x+ 4y = 7)
6x + 7y = 4
simplifying you will be
left with
variables will form zero
variables will form zero
y=#
with a FALSE equation
with a TRUE equation
Solution will take the
0=3
x=#
form of (x, y)
pairs and will leave you
pairs and will leave you
or both rows
-2(3x+ 4y = 7)
3(2x + 7y = 4)
Copyright 2012
Jamie Riggs http://missmathdork.blogspot.com/
0=0
Copyright 2012
Jamie Riggs http://missmathdork.blogspot.com/
Copyright 2012
Jamie Riggs http://missmathdork.blogspot.com/
Copyright 2012
Jamie Riggs http://missmathdork.blogspot.com/