Solve Linear Systems by Substitution

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Solve Linear Systems by Substitution

• Students will solve systems of linear equations
  by substitution.
• Students will do assigned
• homework.
• Students will study
• vocabulary words.

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Lesson 7.2, For use with pages 435-441
Solve the equation.
1. 6a 3 2a 13
2. 4(n 2) n 11
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Daily Homework Quiz
For use after Lesson 7.1
Solve the linear system by graphing.
2x y 3
6x 3y 3
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EXAMPLE 1
Use the substitution method
Solve the linear system
y 3x 2
Equation 1
x 2y 11
Equation 2
SOLUTION
STEP 1
Solve for y. Equation 1 is already solved for y.
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EXAMPLE 1
Use the substitution method
STEP 2
Substitute 3x 2 for y in Equation 2 and solve
for x.
x 2y 11
Write Equation 2.
Substitute 3x 2 for y.
x 2(3x 2) 11
7x 4 11
Simplify.
7x 7
Subtract 4 from each side.
x 1
Divide each side by 7.
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EXAMPLE 1
Use the substitution method
STEP 3
Substitute 1 for x in the original Equation 1 to
find the value of y.
y 3x 2 3(1) 2 3 2 5
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EXAMPLE 1
Use the substitution method
GUIDED PRACTICE
CHECK
Substitute 1 for x and 5 for y in each of the
original equations.
y 3x 2
x 2y 11
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EXAMPLE 2
Use the substitution method
Solve the linear system
x 2y 6
Equation 1
4x 6y 4
Equation 2
SOLUTION
STEP 1
Solve Equation 1 for x.
x 2y 6
Write original Equation 1.
x 2y 6
Revised Equation 1
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EXAMPLE 2
Use the substitution method
STEP 2
Substitute 2y 6 for x in Equation 2 and solve
for y.
4x 6y 4
Write Equation 2.
Substitute 2y 6 for x.
4(2y 6) 6y 4
8y 24 6y 4
Distributive property
14y 24 4
Simplify.
14y 28
Add 24 to each side.
y 2
Divide each side by 14.
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EXAMPLE 2
Use the substitution method
STEP 3
Substitute 2 for y in the revised Equation 1 to
find the value of x.
x 2y 6
Revised Equation 1
x 2(2) 6
Substitute 2 for y.
x 2
Simplify.
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EXAMPLE 2
Use the substitution method
GUIDED PRACTICE
CHECK
Substitute 2 for x and 2 for y in each of the
original equations.
Equation 1
Equation 2
4x 6y 4
x 2y 6
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EXAMPLE 1
for Examples 1 and 2
Use the substitution method
GUIDED PRACTICE
Solve the linear system using the substitution
method.
3x y 10
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EXAMPLE 2
for Examples 1 and 2
Use the substitution method
GUIDED PRACTICE
Solve the linear system using the substitution
method.
x 2y 6
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EXAMPLE 2
for Examples 1 and 2
Use the substitution method
GUIDED PRACTICE
Solve the linear system using the substitution
method.
2x 4y 0