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4.7 Using Cramer

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To use Cramer's Rule on a system of three equations in three variables, you ... One more variable to go! Replace column 2 with the answers to the equations. Ex. ... – PowerPoint PPT presentation

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Title: 4.7 Using Cramer


1
4.7 Using Cramers Rule
  • Algebra 2
  • Mrs. Spitz
  • Fall 2006

2
Objective
  • Use Cramers Rule to solve a system of linear
    equations in three variables.

3
Assignment
  • Pgs. 192-193 4-20 all

4
Introduction
  • You have learned to solve a system of linear
    equations in three variables algebraically and by
    using inverse matrices. In Chapter 3, you
    learned to solve a system of equations in two
    variables by using Cramers Rule. Now you will
    learn to use Cramers Rule to solve a system of
    three equations in three variables.

5
Test for Unique Solutions
  • The system of equations has a unique solution if
    and only if

6
To use Cramers Rule
  • To use Cramers Rule on a system of three
    equations in three variables, you follow the same
    steps as with a system of two equations in two
    variables. The denominator is the DETERMINANT
    containing the coefficients. Then numerators are
    the same determinant except that the coefficients
    of the variable for which you are finding a
    solution are replaced with the constant terms.
    Study this procedure in the following example.

7
Ex. 1 Determine whether the system has a unique
solution. If it does, then solve the system
using Cramers Rule.
Note each determinant in this example is
evaluated by using diagonals.
-3 -4 -8
-644 -(-3)-(-4)-(-8) 17
-6 4 4
8
Ex. 1 Determine whether the system has a unique
solution. If it does, then solve the system
using Cramers Rule.
-9 28 12
4212(-6) -(-9)- 28 - 12 17 1
17
42 12 -6
Since the value of the determinant is not 0, the
system has a unique solution.
17
Replace column 1 with the answers to the
equations.
9
Ex. 1 Determine whether the system has a unique
solution. If it does, then solve the system
using Cramers Rule.
3 6 28
6(-14)(-6) 3 6 - 28 -51 -3
17
6 -14 -6
One more variable to go!
17
Replace column 2 with the answers to the
equations.
10
Ex. 1 Determine whether the system has a unique
solution. If it does, then solve the system
using Cramers Rule.
-21 6 12
9(-6) 28 (-21) 6 - 12 34 2
17
9 -6 28
Finally!
17
Replace column 3 with the answers to the
equations.
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