Transcript 3-2 Solve Systems by Substitution and Elimination

3-2
Using Algebraic Methods
to Solve Linear Systems
To solve a system by substitution, you solve one
equation for one variable and then substitute this
expression into the other equation.
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.
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
For the elimination method, 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.
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.
3x + 5y = –16
2x + 3y = –9
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Find the solution to the system.
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
Example 4: Zoology Application
A veterinarian needs 60 pounds of dog food
that is 15% protein. He will combine a beef
mix that is 18% protein with a bacon mix that
is 9% protein. How many pounds of each does
he need to make the 15% protein mixture?
Let x present the amount of beef mix in the mixture.
Let y present the amount of bacon mix in the mixture.
Holt Algebra 2
Using Algebraic Methods
to Solve Linear Systems
3-2
Example 4 Continued
Write one equation based on the amount of dog food:
Amount of
beef mix
plus
amount of
bacon mix
equals
60.
+
y
=
60
x
Write another equation based on the amount of protein:
Protein of
beef mix
0.18x
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plus
protein of
bacon mix
equals
protein in
mixture.
+
0.09y
=
0.15(60)
3-2
Using Algebraic Methods
to Solve Linear Systems
Check It Out! Example 4
A coffee blend contains Sumatra beans which
cost $5/lb, and Kona beans, which cost
$13/lb. If the blend costs $10/lb, how much
of each type of coffee is in 50 lb of the blend?
Let x represent the amount of the Sumatra beans
in the blend.
Let y represent the amount of the Kona beans in
the blend.
Holt Algebra 2
3-2
Using Algebraic Methods
to Solve Linear Systems
Check It Out! Example 4 Continued
Write one equation based on the amount of each bean:
Amount of
Sumatra beans
plus
x
+
amount of Kona
beans
equals
=
y
50.
50
Write another equation based on cost of the beans:
Cost of Sumatra
beans
5x
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cost of
plus
Kona beans
+
13y
equals
cost of
beans.
=
10(50)
3-2
Using Algebraic Methods
to Solve Linear Systems
Homework pg. 194
#’s 22, 33, 36, 37
Holt Algebra 2