Solving Systems Using Elimination

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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
(For help, go to Lesson 7-2.)
Solve each system using substitution. 1. y 4x
3 2. y 5x 4 3. y 2x 2 y 2x
13 y 7x 20 3x 17 2y
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
1. y 4x 3 y 2x 13 Substitute 4x 3
for y in the second equation.
y 2x 13 4x 3 2x
13 4x 2x 3 2x 2x 13
2x 3 13 2x 16
x 8 y 4x 3 4(8) 3
32 3 29 Since x 8 and y 29, the
solution is (8, 29).
Solutions
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
2. y 5x 4 y 7x 20 Substitute 7x 20
for y in the first equation. y
5x 4 7x 20 5x 4 12x
20 4 12x 24
x 2 y 7x 20 7(2) 20 14
20 6 Since x 2 and y 6, the solution is
(2, 6).
Solutions (continued)
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
3. y 2x 2 3x 17 2y Substitute 2x
2 for y in the second equation. 3x 17
2y 3x 17 2(2x 2) 3x 17 4x
4 7x 17 4 7x 21
x 3 y 2x 2 2(3) 2
6 2 ? 4 Since x 3 and y 4, the solution
is (3, 4).
Solutions (continued)
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
Solve by elimination. 3x 6y 6 5x
2y 14
Step 1 Eliminate one variable.
Step 2 Solve for x. 12x 48 x
4
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
(continued)
Step 3 Solve for the eliminated variable using
either of the original equations.
3x 6y 6 Choose the first
equation. 3(4) 6y 6 Substitute 4 for
x. 12 6y 6 Solve for y.
6y 18 y 3
The solution is (4, 3).
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
Suppose the band sells cans of popcorn for 5
per can and cans of mixed nuts for 8 per can.
The band sells a total of 240 cans and receives a
total of 1614. Find the number of cans of
popcorn and the number of cans of mixed nuts sold.
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
(continued)
Step 1 Eliminate one variable.
Step 2 Solve for n. 3n 414 n
138
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
(continued)
Step 3 Solve for the eliminated variable using
either of the original equations. p
n 240 Choose the first equation. p
138 240 Substitute 138 for n.
p 102 Solve for p.
The band sold 102 cans of popcorn and 138 cans of
mixed nuts.
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
Solve by elimination. 3x 5y 10 5x
7y 10
Step 1 Eliminate one variable.
Step 2 Solve for y. 4y 20 y 5
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
(continued)
Step 3 Solve for the eliminated variable x using
either of the original equations. 3x
5y 10 Use the first equation. 3x
5(5) 10 Substitute 5 for y. 3x 25
10 3x 15
x 5
The solution is (5, 5).
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Solving Systems Using Elimination
ALGEBRA 1 LESSON 9-5
Solve using elimination. 1. 6x 5y 4
2. 7p 5q 2 3x 4y 11 8p
9q 17
(1, 2)
(1, ?1)
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