# Solving Systems of Linear Equations Elimination (Addition)

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3 Steps to Solve Systems of Equations by Addition or Elimination 1. Add or subtract to combine the equations and eliminate one of the variables 2. Solve the resulting equation. 3. Substitute the known value of the first variable (found in step #1) in one of the original equations in the system. 4. Solve this equation for the second variable. 5. Check the solution in both equations of the system. Sample 1 3x + y = 10 2x y = 5 3x + y = 10 Combine by addition (Step 1) 2x y = 5 5x = 15 y variable is eliminated (Step 1) 5x/5 = 15/5 Divide both sides by 5 X = 3 First variable solution (Step 2) 3(3) + y = 10 Substitute the variable into the equation (Step 3) y = 10 9 Subtract 9 from both sides y = 1 Second variable solution (Step 4) Check the solutions (x = 3 and y = 1) in the original equations (Step 5) 3x + y = 10 2x y = 5 3(3) + 1 = 10 2(3) 1 = = = 5 10 = 10 5 = 5 Complete the following system using the steps listed and Sample 1 above: 5x -2y = 30 X + 2y = 6 Solution can be found in step 2 of the lesson.

4 What Do I Eliminate and How? Activity Cut out the boxes with systems of equations and phrases located at the bottom of the sheet. Look at each system and decide which variable would be easier to eliminate. Place the system under the correct variable on the chart. If changes need to be made to the system, include those changes under the category How To. When completed tape or glue each system and how to in the correct column. ELIMINATE x ELIMINATE y HOW TO MULTIPLY BY (-2) 4x + 2y = 8 5x 3y = 4 MULTIPLY BY 3 x + 4y = 7 2x 4y = -3 MULTIPLY BY 2-2x + 3y = 7 2x 5y = -3 x + 2y = 3 -x + y = -2 2x + 5y = 6 -x + 2y = 3 2x 3y = -2 3x + 3y = 4

5 Using Elimination/Addition to Solve Systems of Equations Activity Use elimination/addition to solve the systems of equations listed below. Be sure to show the steps you used to solve each system of equations. 4x + 2y = 8 x + 2y = 3 5x 3y = 4 -x + y = -2 X + 4y = 7 2x + 5y = 6 2x 4y = -3 -x + 2y = 3-2x + 3y = 7 2x 3y = -2 2x 5y = -3 3x + 3y = 4

8 Use the following systems of equations and solutions to create a Math Scavenger Hunt for the students. The solutions in the left column should be placed on the top of the clue cards, and the system next to it should be written on the bottom of the card. Note The solutions do not match the systems they are next to! 2x + y = 7 (3, 0) 3x y = 3 x y = 4 (-4, 3) x + y = 2 2x + 3y = 8 (-1, 3) 3x + y = 5 2x 3y = 8 (3, 2) 2x + 3y = 4 5x + y = 15 (3, -1) 3x + 2y = 9 -x + 2y = 10 (3, -2/3) x 3y = -13 2x 3y = 0 (2, 3) -2x + 2y = -2 y = 3x + 6 (1, 2) 2y = -3x + 3

9 Use the following systems of equations and solutions to create a Math Scavenger Hunt for the students. The solutions in the left column should be placed on the top of the clue cards, and the system next to it should be written on the bottom of the card. 2x + y = 7 (3, 0) 3x y = 3 x y = 4 (-4, 3) x + y = 2 2x + 3y = 8 (-1, 3) 3x + y = 5 2x 3y = 8 (3, 2) 2x + 3y = 4 5x + y = 15 (3, -1) 3x + 2y = 9 -x + 2y = 10 (3, -2/3) x 3y = -13 2x 3y = 0 (2, 3) -2x + 2y = -2 y = 3x + 6 (1, 2) 2y = -3x + 3

### Solving Systems of Linear Equations Elimination (Addition)

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