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System of Equations Elimnation Method

8th grade math

cocoore
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System of Equations Elimnation Method

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  1. February 7, 2022 Good Morning!

  2. Name: ____________________________ Warm-Up Systems of Equations Date-___________________ • How many solutions does the following system of linear equations have? y= -4x -7 y= 4x + 9 • No solutions • One solution • Two solutions • Infinite solutions 2. Solve the system by substitution. Solution: (____,____)

  3. WARM UP ANSWERS • How many solutions does the following system of linear equations have? y= -4x -7 y= 4x + 9 • No solutions • One solution • Two solutions • Infinite solutions

  4. SOLUTION (1, -1)

  5. Click here to watch the video on solving systems using Elimination. Systems of Equations - Elimination

  6. Systems of Equations- Elimination Method Steps • Organize equations by like terms. • Modify one or both equations to create “opposites” for x or y. • Add the equations to eliminate the x or y terms. • Solve for the first variable. • Plug back in to solve for the other variable.

  7. Solving Systems with Linear Combination. Addition and Subtraction (Elimination) Elimination Using Addition 2x + 5y = 11 3x - 5y = 4 -3x + 4y = 12 3x - 6y = 18

  8. Solving Systems with Linear Combination. Addition and Subtraction (Elimination) Elimination Using Addition 2x + 5y = 11 3x - 5y = 4 -3x + 4y = 12 3x - 6y = 18 5x = 15 5 5 x = 3 2x + 5y = 11 2(3) + 5y = 11 6 + 5y = 11 -6 -6 5y = 5 5 5 y = 1 Solution: (3, 1) -2y = 30 -2 -2 y = -15 -3x + 4y = 12 -3x+ 4(-15) = 12 -3x - 60 = 12 • 60 + 60 -3x = 72 -3 -3 x = -24 Solution: (-24, -15)

  9. Elimination Using Subtraction 5x + 2y = 6 9x + 2y = 22 2x - 8y = 12 -4x - 8y = -24

  10. Elimination Using Subtraction 5x + 2y = 6 9x + 2y = 22 2x - 8y = 12 -4x - 8y = -24 Solution: (4, -7) Solution: (6, 0)

  11. Elimination Using Subtraction 5y = 11 - 2x 3x + 5y = 14

  12. 2x + 2y = -2 3x - 2y = 12 Elimination

  13. 6x + 5y = 4 6x - 7y = -20 Elimination

  14. Good Morning! 02/08

  15. Name- __________________________ Warm-Up Elimination Method Directions: Use the elimination method to solve the problems below. Hint: See the steps below if you need help. 1. 2. Systems of Equations- Elimination Method Steps • Organize equations by like terms. • Modify one or both equations to create “opposites” for x or y. • Add the equations to eliminate the x or y terms. • Solve for the first variable. • Plug back in to solve for the other variable

  16. Elimination Using Multiplication Example 1: Multiply One Equation to Eliminate Which variable is easier to eliminate? 3x + 4y = 6 5x +2y = -4 2x - y = 6 3x + 4y = -2 -5x + 3y = 6 x - y = 4

  17. Elimination Using Multiplication Example 2: Multiply Both Equations to Eliminate 3x + 4y = -25 2x - 3y = 6 4x + 5y = 6 6x - 7y = -20

  18. 3x + 2y = 0 X - 5y = 17 Elimination

  19. 4x + 4y = -8 3x -2y = 19 Elimination

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