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Solving systems by

Solving systems by. Combination/Elimination. M8A5. Students will understand systems of linear equations and inequalities and use them to solve problems. b. Solve systems of equations graphically and algebraically, using technology as appropriate. .

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Solving systems by

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  1. Solving systems by Combination/Elimination

  2. M8A5. Students will understand systems of linear equations and inequalities and use them to solve problems. b. Solve systems of equations graphically and algebraically, using technology as appropriate.

  3. Essential Question: How can I use combination/elimination to solve a system of equations?

  4. How would YOU solve this system? { x – y = 4 x + y = 5 Try adding the two equations together… x – y = 4 x + y = 5 What happened to your y’s? + 2x = 9 Super!!! We want only 1 variable.

  5. 2x = 9 Now, solve for x. x = 4.5; good. How do you find y? What is y? Your solution is (4.5, 0.5)

  6. Let’s try another! { -x + 4y = 3 x + 2y = 5 Try adding the two equations together… 1. What happened to your x’s? -x + 4y = 3 x + 2y = 5 + Super!!! We want only 1 variable. 6y = 8

  7. 6y = 8 Now, solve for y. y = ; good. How do you find x? What is x? Your solution is ( , )

  8. Let’s try another! { Try adding the two equations together… 2x + 3y = 4 5x + 3y = -8 2. Are there 2 coefficients that total 0? 2x + 3y = 4 5x + 3y = -8 + Is there something we can do to get 2 coefficients that total 0? What will happen if we multiply the entire 2nd equation by -1? Try it!

  9. 2x + 3y = 4 -1(5x + 3y = -8) 2x + 3y = 4 -5x - 3y = 8 + -3x = 12 What happened? Yes, we eliminated the y’s and now have 1 variable. Solve for x! 3x = 12 -3 - 3 x = -4

  10. Now, substitute x = -4 into either equation to find the value of y. Your solution is ( -4 , 4 ) 2x + 3y = 4 2(-4) + 3y = 4 -8 + 3y =4 8 8 3y = 12 3y = 12 3 3 y = 4

  11. Let’s try another! { 2x - 3y = 4 5x - 3y = 7 Try adding the 2 equations together… 3. Can you add them as they are and eliminate one of the variables? What can we do to change an equation so that by adding we do eliminate a variable?

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