3-2
Using Algebraic Methods
to Solve Linear Systems
Objectives
Solve systems of equations by substitution.
Solve systems of equations by elimination.
The graph shows a system of
linear equations. As you can
see, without the use of
technology, determining the
solution from the graph is not
easy. You can use the
substitution method to find an
exact solution. In substitution,
you solve one equation for one
variable and then substitute
this expression into the other
equation.
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use substitution to solve the system of equations.
y= x–1
x+y=7
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use substitution to solve the system of equations.
y = 2x – 1
3x + 2y = 26
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use substitution to solve the system of equations.
y = 4x –9
y = -2x + 3
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use substitution to solve the system of equations.
2y + x = 4
3x – 4y = 7
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use substitution to solve the system of equations.
5x + 6y = –9
2x – 2 = –y
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
You can also solve systems of equations
with the elimination method. With
elimination, you get rid of one of the
variables by adding or subtracting
equations. You may have to multiply one or
both equations by a number to create
variable terms that can be eliminated.
Reading Math
The elimination method is sometimes called the
addition method or linear combination.
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use elimination to solve the system of equations.
3x + 2y = 4
4x – 2y = –18
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use elimination to solve the system of equations.
4x + 7y = –25
–12x –7y = 19
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use elimination to solve the system of equations.
2x – 3y = -5
-4x + 2y = -10
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use elimination to solve the system of equations.
3x + 5y = –16
2x + 3y = –9
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Use elimination to solve the system of equations.
5x – 3y = 42
8x + 5y = 28
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
In Lesson 3–1, you learned that systems may
have infinitely many or no solutions. When you
try to solve these systems algebraically, the
result will be an identity or a contradiction.
Remember!
An identity, such as 0 = 0, is always true and
indicates infinitely many solutions. A
contradiction, such as 1 = 3, is never true and
indicates no solution.
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Classify the system and determine the number of
solutions.
3x + y = 1
2y + 6x = –18
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Classify the system and determine the number of
solutions.
56x + 8y = –32
7x + y = –4
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Classify the system and determine the number of
solutions.
6x + 3y = –12
2x + y = –6
Holt Algebra 2