Solving Systems of Equations Using Elimination
Objective: Solve systems of linear equations
using elimination
Example 1)
3 x + 2 y = 2 -3 x + 2 y = 6
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Add the equations |
4 y = 8 |
Simplify |
y = 8/4 = 2 |
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Substitute using y = 2 |
3 x + 2(2) = 2 |
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3 x + 4 = 2 |
Simplify |
3 x = -2 |
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x = -2/3 |
Solution (-2/3, 2) |
Example 2)
- x - y = 8 -2 x - y = -1
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Subtract the equations |
x = 9 |
Substitute using x = 9 |
-9 - y = 8 |
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- y = 17 |
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y = -17 |
Solution (9, -17) |
Example 3)
2 x = -3 y + 1 x + 2 y = -1
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Rewrite in standard form |
2 x + 3 y = 1 x + 2 y = -1
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Multiply the 2nd equation by -2 then add |
2 x + 3 y = 1 -2 x - 4 y = 2
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Simplify |
-y = 3 y = -3
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Substitute using y = -3 |
x + 2(-3) = -1 x + -6 = -1
x = 5
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Solution (5, -3) |
Example 4)
3 x + 2 y = 1 2 x - 5 y = -2
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Lets eliminate the x |
-2(3 x + 2 y ) = -2 (1) 3(2 x - 5 y )
= 3(-2)
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Multiply the first equation
by -2 Multiply the 2nd equation by 3
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-6 x - 4 y = -2 6 x - 15 y = -6
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Now add. |
-19 y = -8 y
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Now substitute |
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Simplify. |
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Solution: |
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