Your SlideShare is downloading. ×
  • Like
Alg II 3-5 Sytems Three Variables
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×

Now you can save presentations on your phone or tablet

Available for both IPhone and Android

Text the download link to your phone

Standard text messaging rates apply

Alg II 3-5 Sytems Three Variables

  • 125 views
Published

 

  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
    Be the first to like this
No Downloads

Views

Total Views
125
On SlideShare
0
From Embeds
0
Number of Embeds
0

Actions

Shares
Downloads
1
Comments
0
Likes
0

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide
  • Solution: (4, 2, -3)Solution: (2, -1, 4)Solution: (-1, 2, -4)

Transcript

  • 1. 3-5 Systems withThree VariablesAlgebra II Unit3 Linear Systems© Tentinger
  • 2. Essential Understanding andObjectives• Essential Understanding: To solve systems of three equations in three variables, you can use some of the same algebraic methods you used to solve systems of two equations in two variable.• Objectives:• Students will be able to: • Solve systems of three variables using elimination • Solve systems of three variable using substitution
  • 3. Iowa Core Curriculum• Algebra• Extends A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
  • 4. Three Variable Equations• Two variable equations represent lines• Three variable equations represent planes• Like two variable equations, you can have no solution, one solution, or infinitely many solutions• Graphs of solutions • http://www.mathwarehouse.com/algebra/planes/systems/three- variable-equations.php• No solution: no point lies in all three planes• One Solution: the planes intersect at one common point• Infinitely Many Solutions: The planes intersect at a line
  • 5. Solving a system usingElimination• Step 1: Pair the equations to eliminate one variable, z. Then you will have two equations with two unknowns.• AddSubtract
  • 6. Solving a system usingElimination• 2: Write the new equations as a system. Solve for x and y• Add and solve for y.• Substitute your answer and solve for x
  • 7. Solving a system usingElimination• Step 3: Solve for remaining variable, z. Substitute in answers for x and y into the original equations• Step 4: Write the solution as an ordered triple: (3, 3, 1)
  • 8. Solve using Elimination
  • 9. Solving Equivalent Systems
  • 10. Solving a System usingSubstitution:• Step 1: choose the equation whose variable is easy to isolate.• X+5y=9 x = -5y+9• Step 2: Substitute the expression into the other two remaining equations and simplify• 2(-5y+9) + 3y – 2z = -1 4z – 5(-5y+9) = 4• -7y -2z = -19 25y +4z = 49
  • 11. Solving a System usingSubstitution:• Step 3: Write the two new equations as a system and solve for the remaining variables• use elimination to solve for y then substitute to solve for z• y = 1, z = 6• Step 4: Use the original equation to solve for x• Solution (4, 1, 6)
  • 12. Solve by substitution
  • 13. Application• You manage a clothing store and budget $5400 to restock 200 shirts. You can buy T-shirts for $12 each, polo shirts for $24 each, and rugby shirts for #36 dollars each. If you want to have the same number of T-shirts as polo shirts, how many of each shirt should you buy?• Relate:• T-shirts + polo shirts + rugby shirts = 200• T-shirts = polo shirts• 12 * Tshirts + 24*polo shirts + 36*rugby shirts = 5400• Define:• X = tshirts• Y = polo• Z = rugby
  • 14. Application• You manage a clothing store and budget $5400 to restock 200 shirts. You can buy T-shirts for $12 each, polo shirts for $24 each, and rugby shirts for #36 dollars each. If you want to have the same number of T-shirts as polo shirts, how many of each shirt should you buy?• Write:• Solve:• Substitute x in for equations 1 and 3 then simplify• Write the new equations as a system then solve for y and z• Substitute y and z back into one of the original equations to get x• Solution: (50, 50, 100)
  • 15. Homework• Pg. 171-172• #14-16, 24-26, 32, 34, 37• 9 problems