Solving Systems by Substitution

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Solving Systems by Substitution
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
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Warm Up Solve each equation for x. 1. y x
3 2. y 3x 4 Simplify each expression.
x y 3
2x 10
3. 2(x 5)
4. 12 3(x 1)
9 3x
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Warm Up Continued Evaluate each expression for
the given value of x. 5. x 8 for x 6 6.
3(x 7) for x 10
12
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Objective
Solve linear equations in two variables by
substitution.
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Sometimes it is difficult to identify the exact
solution to a system by graphing. In this case,
you can use a method called substitution.
The goal when using substitution is to reduce the
system to one equation that has only one
variable. Then you can solve this equation by the
methods taught in Unit 1.
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Solving Systems of Equations by Substitution Solving Systems of Equations by Substitution

Step 2
Step 3
Step 4
Step 5
Solve for one variable in at least one equation,
if necessary.
Step 1
Substitute the resulting expression into the
other equation.
Solve that equation to get the value of the first
variable.
Substitute that value into one of the original
equations and solve.
Write the values from steps 3 and 4 as an ordered
pair, (x, y), and check.
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Example 1A Solving a System of Linear Equations
by Substitution
Solve the system by substitution.
y 3x
y x 2
Step 1 y 3x
Both equations are solved for y.
y x 2
Substitute 3x for y in the second equation.
Solve for x. Subtract x from both sides and then
divide by 2.

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Example 1A Continued
Solve the system by substitution.
Write one of the original equations.
Substitute 1 for x.
Write the solution as an ordered pair.
Check Substitute (1, 3) into both equations
in the system.
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Example 1B Solving a System of Linear Equations
by Substitution
Solve the system by substitution.
y x 1
4x y 6
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Example 1C Solving a System of Linear Equations
by Substitution
Solve the system by substitution.
x 2y 1
x y 5
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Check It Out! Example 1a
Solve the system by substitution.
y x 3
y 2x 5
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Check It Out! Example 1b
Solve the system by substitution.
x 2y 4
x 8y 16
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Check It Out! Example 1c
Solve the system by substitution.
2x y 4
x y 7
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Check It Out! Example 1c Continued
Solve the system by substitution.
x 10 7
Step 5
Add 10 to both sides.
x 3
Step 6
(3, 10)
Write the solution as an ordered pair.
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Sometimes you substitute an expression for a
variable that has a coefficient. When solving for
the second variable in this situation, you can
use the Distributive Property.
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Example 2 Using the Distributive Property
y 6x 11
Solve by substitution.
3x 2y 5
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Example 2 Continued
y 6x 11
Solve by substitution.
3x 2y 5
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Check It Out! Example 2
2x y 8
Solve by substitution.
3x 2y 9
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Example 2 Consumer Economics Application
Jenna is deciding between two cell-phone plans.
The first plan has a 50 sign-up fee and costs
20 per month. The second plan has a 30 sign-up
fee and costs 25 per month. After how many
months will the total costs be the same? What
will the costs be? If Jenna has to sign a
one-year contract, which plan will be cheaper?
Explain.
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Check It Out! Example 3
One cable television provider has a 60 setup fee
and 80 per month, and the second has a 160
equipment fee and 70 per month.
a. In how many months will the cost be the same?
What will that cost be.
b. If you plan to move in 6 months, which is
the cheaper option? Explain.
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Lesson Quiz Part I
Solve each system by substitution. 1. 2.
3.
y 2x
(2, 4)
x 6y 11
(1, 2)
3x 2y 1
3x y 1
x y 4
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Lesson Quiz Part II
4. Plumber A charges 60 an hour. Plumber B
charges 40 to visit your home plus 55 for each
hour. For how many hours will the total cost for
each plumber be the same? How much will that cost
be? If a customer thinks they will need a plumber
for 5 hours, which plumber should the customer
hire? Explain.
8 hours 480 plumber A plumber A is cheaper
for less than 8 hours.