y 2 10 x y 3 x 10 3. Combine the two models. Remove - - PowerPoint PPT Presentation

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y 2 10 x y 3 x 10 3. Combine the two models. Remove - - PowerPoint PPT Presentation

Jul 06, 2023 17 likes •350 views

D AY 82 E LIMINATION U SING THE ADDITION PROPERTY OF EQUALITY 1. Let x represent the number of correct answers. Let y represent the incorrect answers. Write a system of equations. Janets scoring Matthews scoring system system 2

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SLIDE 1

DAY 82 – ELIMINATION

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SLIDE 2

USING THE ADDITION PROPERTY OF

EQUALITY

  • 1. Let x represent the number of correct answers. Let y

represent the incorrect answers. Write a system of equations. Janet’s scoring system Matthew’s scoring system 2 spaces for a correct answer 1 space forward for + an incorrect answer 3 spaces for a correct answer 1 space backward for + an incorrect answer 10 spaces forward 10 spaces forward ? + ? =10 ? + ? =10

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SLIDE 3

USING THE ADDITION PROPERTY OF

EQUALITY

  • 1. Let x represent the number of correct answers. Let y

represent the incorrect answers. Write a system of equations. Janet’s scoring system Matthew’s scoring system 2 spaces for a correct answer 1 space forward for + an incorrect answer 3 spaces for a correct answer 1 space backward for + an incorrect answer 10 spaces forward 10 spaces forward 2x + y = 10 3x + (-y) = 10

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SLIDE 4
  • 2. Rewrite the equation representing Matthew's

scoring system using a minus sign. Model this system of equations using the x-tiles and y-tiles.

10 2   y x

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SLIDE 5

10 3  y x

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SLIDE 6
  • 3. Combine the two models. Remove neutral pairs, and

write the new equation.

10 10 ) 3 ( ) 2 (      y x y x

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SLIDE 7
  • 3. Combine the two models. Remove neutral pairs, and

write the new equation. 5x = 20

10 10 ) 3 ( ) 2 (      y x y x

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SLIDE 8
  • 4. Which variable was eliminated? Why?

Solve the resulting equation for the remaining variable.

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SLIDE 9
  • 4. Which variable was eliminated? Why?

Solve the resulting equation for the remaining variable.

4 x pairs; neutral variable; = y 

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SLIDE 10
  • 5. Use substitution in either of the original

equations to find the value of the variable that was eliminated by removing neutral

  • pairs. The solutions to the system is (?,?).
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SLIDE 11
  • 5. Use substitution in either of the original

equations to find the value of the variable that was eliminated by removing neutral

  • pairs. The solutions to the system is (?,?).

) 2 , 4 (

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SLIDE 12
  • 6. Henry answered _?_ questions

correctly and _?_ questions incorrectly.

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SLIDE 13
  • 6. Henry answered _?_ questions

correctly and _?_ questions incorrectly. 4 correctly , 2 incorrectly

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SLIDE 14

USING THE SUBTRACTION PROPERTY OF EQUALITY

1.

Use the x-titles and y-titles to model the system

       4 10 4 y x y x

10 4   y x

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SLIDE 15

4  y x

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SLIDE 16
  • 2. Combine the two models, remove any

neutral pairs. Is a variable eliminated? Why or why not?

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SLIDE 17
  • 2. Combine the two models, remove any

neutral pairs. Is a variable eliminated? Why or why not?

no variable are eliminated because neither combines with an equal number of opposites.

14 2 5   y x

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SLIDE 18
  • 3. Use tiles to model the system of

equations again.

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SLIDE 19
  • 4. You can eliminate the y-variable in this

system by using the Subtraction Property of

  • Equality. Recall that to subtract, you add

the opposite. First model the opposite of the equation x + y = 4.

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SLIDE 20

4  y x

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SLIDE 21

4 ) 4 ( 1 ) ( 1         y x y x

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SLIDE 22
  • 5. Now subtract by adding the opposite. Combine the

model of the opposite of x + y = 4 with the model of 4x y = 10, and remove neutral pairs. What is the resulting equation? What variable was eliminated?

) 4 ( 10 ) ( ) 4 (        y x y x

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SLIDE 23

6.Use the model to solve the resulting equation for x.

  • 7. Substitute the solution for x into one
  • f the original equations, and solve

for y.

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SLIDE 24

6.Use the model to solve the resulting equation for x.

  • 7. Substitute the solution for x into one
  • f the original equations, and solve

for y.

2  x

2  y

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SLIDE 25

8.Check your solution in both of the

  • riginal equations.

9.Describe how to solve a system of equation using the Subtraction Property of Equality.

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SLIDE 26

8.Check your solution in both of the

  • riginal equations.

9.Describe how to solve a system of equation using the Subtraction Property of Equality.

) ( 10 2 8 ) ( 4 2 2 true and true    

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SLIDE 27

SOLVE THE SYSTEM USING THE

ELIMINATION METHOD.

        22 5 4 4 5 2 y x y x

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SLIDE 28

The coefficients of the y-terms are opposites. By adding the equations, you can eliminate the y-term. This leaves an equation with only one variable, which you can solve for x.

3 18 6 22 5 4 4 5 2        x x y x y x

Add the equations, Solve for x

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SLIDE 29

To find y, substitute 3 for x in either of the original equations.

y y y y x y for Solve 2 sides. both to 6 Add 10 5 Simplify. 4 5 6 1 Equation in for Substitute 4 5 ) 3 ( 2           

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SLIDE 30

Check the solution, (3,-2), in both original equations. If the coefficients of the variable you want to eliminate are identical, subtract the

  • equations. If the equations are not in

standard form Ax + By = C, begin by writing them in standard form.

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SLIDE 31

SOLVE BY THE ADDITION METHOD:

       2 5 2 1 10 3 y x y x

Since the coefficients of the y terms are additive inverses, adding the corresponding sided of the equations will eliminate the y terms.

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SLIDE 32

2 Equation in

  • r

1 Equations in 3

  • n

Substituti 3 3 2 15 5 5 2 1 10 3        x x x y x y x

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SLIDE 33

4 1 y 10 y 3(3) 1 10 y 3x 3 1       y

     1 3 y x

Thus, Is an equivaltent system