Transcript Chapter 9
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