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Chapter 9
Systems of Linear
Equations
Section 9-1
The Graphing Method
System of Equations
Two or more equations in
the same variables
Solution of a System
All the ordered pairs that make
both equations true
This point is where the two
lines intersect
To Solve Using Graphing:
 Graph
both lines in the same
coordinate plane
 The point where the lines
intersect is the solution to the
system
Continued
 If
the lines do not intersect,
there is no solution
 If the lines coincide, there are
infinitely many solutions
Example 1
Solve the system by graphing
2x – y = 8
x+y=1
Example 2
Solve the system by graphing
x – 2y = -6
x – 2y = 2
Example 3
Solve the system by graphing
2x + 3y = 6
4x + 6y = 12
Section 9-2
The Substitution
Method
To Solve Using Substitution:
 Solve
one equation for one of
the variables
 Substitute this expression in
the other equation and solve
Continued
 Substitute
this value in the
first equation to solve for the
second variable
Example 1
Solve using substitution
method
x + y = 15
4x + 3y = 38
Example 2
Solve using the substitution
method
2x – 3y = 4
x + 4y = -9
Example 3
Solve using substitution
method
y/2 = 2 – x
6x + 3y = 12
Section 9-4
The Addition-orSubtraction Method
To Solve using Add-or-Subtract:
 Add
or subtract the equations to
eliminate one variable
 Solve the resulting equation for
the other variable
 Substitute in either equation to
find the value of the first
variable
Example 1
Solve using the Addition
method
5x – y = 12
3x + y = 4
Example 2
Solve using the subtraction
method
6c + 7d = -15
6c – 2d = 12
Example 3
Solve using addition or
subtraction
3r + 2s = 2
3r + s = 7
Section 9-5
Multiplication with the
Addition-or-Subtraction
Method
Example 1
Solve using multiplication
4x – 5y = 23
3x + 10y = 31
Example 2
Solve using multiplication
3a +4b = 2
5a + 9b = 1
Example 3
Solve using multiplication
5x/3 + y = 7
x + y/4 = 7/2
Example 4
Solve using multiplication
4s – 5t = 3
3s + 2t = -15