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Mastering Elimination Method in Solving Systems of Equations

Welcome back! Today, we will focus on warming up our math skills using the elimination method with multiplication to solve systems of equations. Get ready to use whiteboards for a hands-on approach! We will tackle examples, find answers, and solve various problems together. With practice problems and engaging exercises, this session aims to enhance your understanding and application of the elimination method. Let’s dive into the world of mathematics and make learning fun!

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Mastering Elimination Method in Solving Systems of Equations

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  1. Welcome back…. Let’s warm up! 1) 4x + 5y = 12 2) 3x – 2y = 12 4x + 3y = 4 4x + 2y = 2

  2. 8-4 Elimination Using Multiplication Objective: To solve systems of equations using the Elimination method with Multiplication **Let’s use whiteboards today!

  3. Example 1 – on paper 2x + y = 5 3x – 2y = 4 7x = 14 x = 2 2(2) + y = 5 4 + y = 5 y = 1 ( ) 2 = 4x + 2y = 10 3x – 2y = 4 ANSWER: (2,1)

  4. 1) -3x – 4y = 2 -2x + y = -6 Answers: 1. (2,-2) 2. (5,-2) 3. Infinitely Many On a white board!! 2) 3x – 2y = 19 5x + 4y = 17 3) x – 2y = -1 -2x + 4y = 2

  5. Example 2 – on paper 0 = -y + 4 y = 4 3x = 2(4) – 2 3x = 8 – 2 3x = 6 x = 2 9x = 5y – 2 9x = 5y – 2 3x = 2y – 2 ( ) -3 = -9x = -6y + 6 ANSWER: (2,4)

  6. EXAMPLE 3 – on whiteboard ( )4 ( )3 2x – 3y = 2 5x + 4y = 28 What do we eliminate? y! 2(4) – 3y = 2 8 – 3y = 2 -3y = -6 y = 2 8x – 12y = 8 15x + 12y = 84 23x = 92 x = 4 ANSWER (4,2)

  7. EX4: 2x + 3y = 5 5x + 4y = 16 Answer: (4,-1) Eliminate x 1st times 5 2nd times -2 10x + 15y = 25 -10x – 8y = -32 7y = -7 y = -1 Eliminate y 1st times 4 2nd times -3 8x + 12y = 20 -15x – 12y = -48 -7x = -28 x = 4

  8. Try with a mathlete: 1) 3x + 5y = 11 2x + 3y = 7 2) 2x – 3y = 8 -5x + 2y = 13

  9. Homework: • Pg. 479 # 15 – 31 odd

  10. Math Lab Systems of Equations Review **Let’s use whiteboards today!

  11. Substitution • y = 3x x + 2y = -21 Answers: 1) (-3,-9) 2) (3,0) y = 2x – 6 3x + 2y = 9

  12. Elimination 1) -3x + 4y = 12 2) x + y = 8 3x – 6y = 18 x – y = 4 (-24,-15) (6,2)

  13. 1) -3x – 4y = 2 -2x + y = -6 Answers: 1. (2,-2) 2. Infinitely Many Elimination with Multiplication 2) x – 2y = -1 -2x + 4y = 2

  14. Elimination with Multiplication 1) 4x + 3y = 19 3x – 4y = 8 Answer: (4,1) 2) 4x – 7y = 10 3x + 2y = -7 Answer: (-1,-2)

  15. Even More Practice  Solve using any method: Shall we race?? 1) 7x + 3y = -1 4x + y = 3 2) 3x + 4y = 10 6x + 8y = 5 3) x – y = 2 2x – 3y = 5

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