31 GRAPHING SYSTEMS OF EQUATIONS

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3-1 GRAPHING SYSTEMS OF EQUATIONS

• Define
• System of equations
• Common solutions
• Graph descriptions
• Consistent and independent
• Consistent and dependent
• Inconsistent

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• C. Solving Methods
• Graphing
• Substitution
• Elimination
• D. Steps for graphing
• Graph both on same graph
• Find point of intersection

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• C. Examples
• 2x 3y 12
• 2x y 4
• 9x 8y 8

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3-2 SOLVING SYSTEMS OF EQUATIONS USING ALGEBRA

• Substitution
• Solve one equation for x
• Sub. into other equation
• Solve for y
• Sub. y into an equation
• Solve for x
• Check

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• B. Elimination
• Line-up like-terms and
• Add down
• Solve
• Sub. Into an equation
• Solve
• Check in both equations

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• C. Examples
• 2x y 10
• 3x y 5
• 2.

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3-3 CRAMERS RULE

• Define
• Cramers rule
• Determinants
• Elements
• Second-order determinants

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• B. Value of a determinant
• C. Cramers Rule

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• D. Examples
• 1. Find the determinant value.
• 2. Solve using Cramers Rule

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3-4 GRAPHING SYSTEMS OF INEQUALITIES

• Define Systems of Inequalities
• Solving systems of inequalities
• Graph all inequalities on same graph

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• C. Examples

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3-5 LINEAR PROGRAMMING

• Define
• Linear programming
• Constraints
• Feasible region
• Unbounded
• Max Min Values

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• B. Find the max min values
• Graph each inequality
• Find the vertices
• Plug-in each vertex into the function
• C. Example
• x - 3y gt -7 5x y lt 13 x 6y gt-9
• 3x 2y gt -7 f(x,y) x y

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3-6 APPLICATIONS OF LINEAR PROGRAMMING

• Linear Programming Procedure
• Steps 1-7 (P. 160)
• B. Example
• P. 163 (8)

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3-7 SOLVING SYSTEMS OF EQUATIONS IN THREE
VARIABLES

• Review elimination
• Review substitution

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• C. Steps
• Use elimination on equation 1 2
• Use elimination on equation 2 3
• Use elimination on the two new equations
• 4. Use substitution to find the other two
  variables
• Check in all three equations
• D. Examples