Solve System by Linear Combination / Addition Method

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Solve System by Linear Combination / Addition
Method

• Objectives
• To solve a system of equations using the Linear
  Combination Method

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Example 1
Solve using the addition method.
x y 7 x y 3
x y 3
5 y 3
2x 0y 10
y -2
2x 10
x 5
(5,-2)
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Example 2
Solve using the addition method.
2x 3y 11 -2x 9y 1
2x 3y 11
2x 3(1) 11
0x 12y 12
2x 3 11
12y 12
2x 8
y 1
x 4
(4,1)
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Practice
Solve using the addition method.
1)
2)
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Example 3
Solve using the addition method.
3x y 8 x 2y 5
write in standard form
3x y 8
multiply as needed
( ) ( )
(-3)
(-3)
x 2y 5
3x y 8
-3x 6y -15
addition property
-7y -7
3x - (1) 8
y 1
3x 9
x 3
(3,1)
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Example 4
Solve using the addition method.
8x 2y -10
write in standard form
( ) ( )
4x 3y 15
multiply as needed
(-2)
(-2)
8x 2y -10
addition property
-8x 6y -30
8x 2(-5) -10
8y -40
8x - 10 -10
y -5
8x 0
x 0
(0,-5)
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Practice
Solve using the addition method.
1)
2)