Systems of Linear Equations The Substitution Method.
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Transcript of Systems of Linear Equations The Substitution Method.
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Systems of Linear EquationsThe Substitution Method
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Previous Lessons0You have already learned the following…0How to solve equation with two variables0Set up and solve a function table0Input vs. output0Ordered pair solution is where the two
linear equation intersect on a coordinate plane
0How to solve using the Elimination Method
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“Substitution”0What does it mean to
substitute?
0Definition: In Algebra "Substitution" means putting numbers where the letters are.
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Using the Substitution Method
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Example 1Equation One x + y = 8Equation Two x + 2y = 10
Step 1: Select one equation. Solve for one variable to be isolated on one side of the equal sign.
x + y = 8subtract y from both sides -y -y
x = 8 - y
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Step 2: Substitute this expression into the second equation to find the value of the
one variable.
Equation one: x = 8 – y
Equation two: x + 2y = 10New equation: (8 – y) + 2y = 10
Combine like Terms (8 – y) + 2y = 10 8 + y = 10
Subtract 8 -8 -8y = 2
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Step 3: Substitute this value to find the value of the other variable.
y = 2
x + y = 8
x + 2 = 8
Subtract 2 -2 -2
x = 6
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Final Solution:
( 6, 2 )
Check: Plug both values into one of the original equations.
x + y = 86 + 2 = 8 8 = 8
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Copy and Solve
Complete these problems for homework and we will review tomorrow