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Algebra II Recipe: Solving Systems with Three Unknown Variables
A. Steps for Solving the System Algebraically
  1. Choose 2 different pairs of equations of the 3 given equations; for example: Eq1 and Eq2 paired with Eq1 and Eq3 OR Eq1 and Eq2 paired with Eq2 and Eq3
  2. Use the multiplication-addition method to eliminate the same variable in each pair of equations.
  3. Use the 2 resulting equations to eliminate one of the two remaining variables using the multiplication-addition method. This will result in finding the value of one of the variables.
  4. Substitute the value found in step 3 into one of the equations with only two variables.
  5. Now that you know the value of 2 variables, substitute these values into one of the equations with 3 variables to find the value of the third variable.
  6. List the values in a set of parentheses in alphabetical order (x, y, z) for the answer.
ExamplesExamples:
2x + y - z = 2
3x + 2y + 3z = 17
5x - y + 2z = 15

Click to see the solution process for this problem.

B. Steps for Solving Using Inverse Matrices
  1. Set up a matrix equation AX = B.
  2. Enter matrix A and matrix B into the calculator.
  3. Type A-1ยท B into the calculator to get the answer.
Companion Exercises Practice Problems


G Redden

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