5.3 Systems of Linear Equations in Three Variables - PowerPoint PPT Presentation

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5.3 Systems of Linear Equations in Three Variables

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5.3 Systems of Linear Equations in Three Variables A of a system of linear equations in three variables is an of real numbers that satisfies all equations ... – PowerPoint PPT presentation

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Title: 5.3 Systems of Linear Equations in Three Variables


1
5.3 Systems of Linear Equations in Three
Variables
2
  • A of a system of linear equations in three
    variables is an
  • of real numbers that satisfies all
    equations of the system.
  • In other words, the solution is the point of
  • of three planes.

solution
ordered
triple
intersection
3
Solving Linear Combination Method
  • 1. Use the linear combination method to rewrite
    the linear system in three variables as a linear
    system in two variables.
  • Combine two of the equations to eliminate one
    variable, then combine another two equations to
    eliminate the same variable.
  • 2. Solve the new linear system for both of its
    variables.
  • 3. Substitute the values found in step 2 into one
    of the original equations and solve for the
    remaining variable.

4
Solve the system of linear equations.
  • 1.

5
Solve the system of linear equations.
  • 2.

6
  • A system of linear equations in three variables
    can also have solutions. This happens when
    one of the following
  • 1. three different planes intersect in a single
    line
  • 2. two coinciding planes intersect in a third
    plane
  • 3. three coinciding planes.

infinite
7
  • A system of linear equations in three variables
    can also have solution. This happens when one
    of the following
  • 1. three parallel planes
  • 2. two coinciding planes parallel to a third
    plane
  • 3. three planes intersecting in three parallel
    lines
  • 4. two parallel lines intersecting a third plane
    in two parallel lines

no
8
Solve the system of linear equations.
  • 3.

9
Solve the system of linear equations.
  • 4.
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