Algebra 2

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Algebra 2

• Section 3-3
• Cramers Rule

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What Youll LearnWhy Its Important

• To find the values of second-order determinants,
  and
• To solve systems of equations by using Cramers
  rule

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Cramers Rule

• Another method for solving systems of equations
  is Cramers rule.
• The rule gives us quick way to find the
  solution to a system of two equations with two
  variables.
• It is especially useful when the coefficients are
  large or involve fractions or decimals.
• Cramers rule makes use of determinant's
• A determinant is a square array of numbers or
  variables enclosed between two parallel vertical
  bars.
• The numbers or variables within a determinant are
  called elements.

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Determinant

• The determinant below has two rows and two
  columns and is called a second-order determinant.

rows
columns
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Value of a Second-Order Determinant
Notice that the value of the determinant is found
by calculating the difference of the products of
the two diagonals
bc
ad-bc
ad
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Example 1

• Find the value of each determinant
• A. B.

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Solution Example 1A

• Find the value of each determinant
• A.

3(6) 5(2)
18 10
8
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Solution Example 1B

• Find the value of each determinant
• B.

-2(8) 7(5)
-16 35
-51
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Example 2

• Solve the following system using Cramers Rule
• Both equations must be in standard form
• 2x 3y 9
• X 5y -2

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Solution Example 2
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THE END