Download Elimination

10.3 Solving Linear
Systems
Elimination
Method #3
All 3 Methods
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Graphing
Substitution
Elimination
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Using addition/subtraction
Using multiplication
Solutions
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One solution
No solution
Infinitely many solutions
Elimination
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We will try to eliminate one variable by adding,
subtracting, or multiplying the variable(s)
until the two terms are additive inverses.
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We will then add the two equations, giving us
one equation with one variable.
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Solve for that variable.
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Then insert the value into one of the original
equations to find the other variable
Elimination
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The key to solving a system by elimination is getting
rid of one variable.
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Let’s review the Additive Inverse Property.
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What is the Additive Inverse of: 3x? -5y? 8p? q?
-3x 5y -8p -q
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What happens if we add two additive inverses?
We get zero. The terms cancel.
Elimination
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Solve the system:
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Notice that the n terms in both equations are additive
inverses. So if we add the equations the n terms will cancel.
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So let’s add & solve:
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m+n=6
m -n=5
m+n=6
+ m- n=5
2m + 0 = 11
2m = 11
m = 11/2 or 5.5
Insert the value of m to find n: 5.5 + n = 6
n = .5
The solution is (5.5, .5).
Elimination
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Solve the system: 3s - 2t = 10
4s + t = 6
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We could multiply the second equation by 2 and the t terms would be
inverses OR We could multiply the first equation by 4 and the second
equation by -3 to make the s terms inverses.
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Let’s multiply the second equation by 2 to eliminate t. (It’s easier.)
3s - 2t = 10
3s – 2t = 10
2(4s + t = 6)
8s + 2t = 12
Add and solve:
11s + 0t = 22
11s = 22
s=2
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Insert the value of s to find the value of t
The solution is (2, -2).
3(2) - 2t = 10
t = -2
Elimination
Solve the system by elimination:
1.
-4x + y = -12
4x + 2y = 6
2.
5x + 2y = 12
-6x -2y = -14
3.
5x + 4y = 12
7x - 6y = 40
4.
5m + 2n = -8
4m +3n = 2