3.2 Solve Linear Systems Algebraically Fri Oct 28

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3.2 Solve Linear Systems AlgebraicallyFri Oct 28

• Do Now
• Solve the system by graphing
• 1) X y 2
• 2x y 3

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HW Review p.156 3-21 odds

• 3) (1,-1) 19) no solution inconsistent
• 5) (4,-1) 21) infinitely many consistent
• 7) (5,0) and dependent
• 9) (-2,4)
• 11) infinitely many solutions
• 13) (3,3)
• 15) C (1,-6)
• 17) (2,-1) consistent and independent

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HW Review 23-29 odds

• 23) (2,0) consistent and independent
• 25) (3, -1) consistent and independent
• 27) infinitely many consistent and dependent
• 29) A

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Solving Linear Systems

• There are 2 ways to solve a linear system
  algebraically
• The Substitution Method
• The Elimination Method
• It is important to note to ALWAYS check your
  answers by plugging into one of the equations

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Substitution Method

• Step 1 Solve one of the equations for one of its
  variables
• Step 2 Substitute the expression from Step 1
  into the other equation and solve for the other
  variable
• Step 3 Substitute the value from Step 2 back
  into Step 1 equation to solve the last variable

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Ex Substitution

• Solve the system using substitution
• 2x 5y -5
• X 3y 3
• Step 1 Solve equation 2 for x
• X -3y 3
• Step 2 Substitute the X equation into the other
  equation and solve for Y
• 2x 5y -5
• 2(-3y 3) 5y -5
• -6y 6 5y -5
• Y 11
• Step 3 Substitute the value of y back into Step
  1
• X -3y 3
• X -3(11) 3
• X -30

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Elimination Method

• Step 1 Multiply one or both of the equations by
  a constant to obtain coefficients that are
  opposite (Least common multiple)
• Step 2 Add the two equations together and solve
  for the variable that doesnt cancel
• Step 3 Substitute the value obtained into either
  equation and solve for the other variable

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Ex Elimination

• Solve the system using the elimination method
• 3x - 7y 10
• 6x - 8y 8
• Step 1 Multiply Equation1 by -2 so the x
  coefficients are opposite
• -6x 14y -20
• 6x - 8y 8
• Step 2 Add the 2 equations together and solve
  for y
• 6y -12
• Y -2
• Step 3 Substitute back into y and solve for x
• 3x - 7(-2) 10
• 3x 14 10
• 3x -4 x -4/3

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Infinite or no solutions

• When solving a system, we could get infinitely
  many or no solutions
• Infinitely many solutions a true statement
• Ex 2 2
• No solutions a false statement
• Ex 12 8

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You try

• Solve the linear system using either substitution
  or elimination
• 1)
• 2)
• 3)
• 4)

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Closure

• Journal Entry Which method of solving systems
  algebraically do you like better? Why? Explain
  how to solve using that method
• HW p.164 3-39 odds

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3.1-3.2 PracticeMon Oct 31

• Do Now
• Solve the linear systems
• 1) 3x 2y 1
• -2x y 4
• 2) 8x 2y 4
• -2x 3y 13

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HW Review p.164 3-39 odds

• 3) (6,-1) 23) no solution
• 5) no solution 25) (7, 3)
• 7) (4/3, 2) 27) did not multiply whole
  equation by -2
• 9) (0,3) 29) (-5, -6)
• 11) (-3, 8 ) 31) infinitely many
• 13) (44, -17) 33) (-8, 0)
• 15) (7, 1/2) 35) (7, -6)
• 17) (-6, -2) 37) (-3/2, 4)
• 19) (-1/2, 1/6) 39) (-3/4, 1/2)
• 21) (-8, 6)

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Worksheet 3.1 and 3.2

• 3.1 4-12
• 3.2 1-21

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Closure

• Hand in Solve the linear system by either the
  substitution or elimination method
• 3x 7y -1
• 2x 3y 6
• HW Finish worksheets