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4.7 Using Cramer’s Rule

4.7 Using Cramer’s Rule. Algebra 2 Mrs. Spitz Fall 2006. Objective:. Use Cramer’s Rule to solve a system of linear equations in three variables. Assignment. Pgs. 192-193 #4-20 all. Introduction.

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4.7 Using Cramer’s Rule

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  1. 4.7 Using Cramer’s Rule Algebra 2 Mrs. Spitz Fall 2006

  2. Objective: • Use Cramer’s 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 Cramer’s Rule. Now you will learn to use Cramer’s 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 Cramer’s Rule • To use Cramer’s 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 Cramer’s Rule. Note: each determinant in this example is evaluated by using diagonals. -3 -4 -8 =-6+4+4-(-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 Cramer’s Rule. -9 28 12 =42+12+(-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 Cramer’s 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 Cramer’s 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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