7.3  Solving Linear Systems by Linear Combination

Mrs. Agriesti's Algebra

Goal: To use linear combination to solve systems of linear equations.

Examples:

Step 1:  These equations are in standard form.



Step 2:  Multiply the first equation by the second equation's x coefficient and the second equation by the first equations x coefficient.




Step 3:  Distribute a negative on the second equation.


Step 4&5:  Add the equations together.  The x is eliminated.  Solve for y.

Step 6:  Substitute the answer you found in step 5 into one of the original equations.  Solve for the other variable.







Step 7:  Check your answers in BOTH original equations.









Step 8:  Write your answer as an ordered pair.  (Use alphabetical order.)

(-1, 2)

(0, -3)