Nov. 9 Soving Systems Involving Two Variables
Transcript of Nov. 9 Soving Systems Involving Two Variables
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The number of gold medals won by women w, and men m, is related by the following equations
w + m = 7 w m = 1
If we write them both in terms of w then
w = 7 m
and
w = 1 + m
is our system, we can solve it graphically
So we can check our solution by substituting it into each equation, and the left side should equal the right side!!
w = 7 m
4 = 7 3
4 = 4
and w = 1 + m
4 = 1 + 3
4 = 4
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Solving a System by Addition or Subtraction of the Equations....Elimination of a Variable
We manipulate the equations so when we add them together we can eliminate one of the variables.
4x + 3y = 12
4x y = 4
In this example we can subtract the two equationsto eliminate the x variable
We then solve for y and can substitute back into either equation to find the value for x
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Solve by addition or subtraction of the equations:
x + 4y = 62x 3y = 1
( 2, 1 )
notice that if you add them or subtract them without manipulating them you will not get rid of either the x or y variables
First we need to multiply one or both of the equations by some number or numbers that will result in a common variable coefficient for either x or y
x + 4y = 6
2x 3y = 1
We always want to get to the point where we can eliminate one variable
Solve for the variable you have left
Substitute into one of the equations to find the other variable's solution
Check by substituting both variable solutions into the equations
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3x + 2y = 2
4x + 5y = 12
Solve by elimination:
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Find the exact solution by Substitution:
5x 3y 2 = 0
7x + y = 0
1. Solve for one variable in terms of the other.
2. Substitute this into the other equation to eliminate the variable.
3. Solve for the one variable that is left after the elimination.
4. Use this in one of the equations to find the second variable.
5. Check your answer
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Solve by Substitution:
3x + 2y = 19
5x 2y = 5
1. Solve for one variable in terms of the other.
2. Substitute this into the other equation to eliminate the variable.
3. Solve for the one variable that is left after the elimination.
4. Use this value in one of the equations to find the second variable.
5. Check your answer
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Inconsistent Systems SolutionsParallel Lines
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Dependent System SolutionsSame line
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= 1
+ = 1
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exercise 24
Questions 1 6