Objective:

To use linear combination to solve systems of linear equations.

Notes:

Steps to solve a system of equations by linear combination.
  1. Make sure both equations are in standard form.
  2. Multiply the first equation by the coefficient of the first variable of the second equation and the second equation by the coefficient of the first variable of the first equation.
  3. Distribute a negative so that one coefficient is positive and the other negative.
  4. Add the equations together. The first variable will cancel and be eliminated.
  5. Solve for the second variable.
  6. Substitute the answer from step 5 into one of the original equations and solve for the remaining variable.
  7. Check the answers in BOTH equations
  8. Write your answer as an ordered pair. (Use alphabetical order.)

Examples:

Find the solution by using linear combination.

  1. Ex 1


  2. Ex 2

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