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Systems of EquationsBy: China King

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ELIMINATION METHOD

SUBSITUTION METHOD

QUIZ

In the elimination method you add or subtract the equations to get an equation in one variable.

Example3y+2x=65y-2x=10

Elimination

We can eliminate the x-variable by adding the two equations together

STEP 1

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We can now solve for the y- variable.Example3y+2x=6

+ 5y-2x=108y=16

Elimination

STEP 2

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We can divide both sides of the equation by 8.

Example8y=168 8Y=2

Elimination

STEP 3

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Now that we know that y=2. We substitute that answer into the other equation to solve for the x-variable.

Example3y+2x=6

3(2)+2x=66+2x=6

Elimination

STEP 4

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Subtract 6 from both sides.Example6+2x=6-6 -6

2x=0

Elimination

STEP 5

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Divide by -2 on both sidesExample

2x=02 2 X=0

Elimination

STEP 6

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Example3y+2x=6

+ 5y-2x=10

The solution to the following problem isX=0 Y=2

(0,2)

Elimination

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Elimination

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Q1: What was the first step in the elimination process?

Quick Check #1

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a) Multiply by 2

b) Add the equations together

c) Subtract the two equations

d) I have no clue

The first step in the elimination process was to add the two equations together.

CORRECT !!!

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Video #2

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Q1: What was the last step in the elimination process?

Quick Check #2

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a) Check your answer

b) Divide by 2

c) Graph the answer

d) I have no clue

The last step in the elimination process was to check your answer.

CORRECT !!!

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Q3: Solve the following system of equation.x+2y=43x+y=2

Quick Check #3

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a) (2,0)

b) (1,-1)

c) (0,2)

The answer is (0,2). You are a master of the elimination method!!!

CORRECT !!!

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We use the substitution method by solving one of the equations for one of the variables. This method is used when it isn’t easy to use the elimination method.

Substitution

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Substitution

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Q1: What was the first step in the substitution process?

Quick Check #1

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a) Substitute for x

b) Substitute for y

c) Graph the answer

d) I have no clue

The first step in the substitution process was to substitute for x.

CORRECT !!!

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Substitution

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Q1: What was the last step in the substitution process?

Quick Check #2

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a) Multiply by 2

b) Check your answer

c) Subtract the two equations

d) I have no clue

The last step in the substitution process was to check your answer.

CORRECT !!!

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Q3: Solve the following system of equation by using substitution.

X-2y=-10Y=3x

Quick Check #3

a) (6,2)

c) (0,0)

b) (2,6)

The answer is (2,6). You are a master of the substitution method!!!

CORRECT !!!

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Start Quiz

Quiz

Time!

Quiz Time!Quiz Time!

Quiz Time!

QUIZ TIME!

Q1: Solve the following problem using the elimination method.

-4x-2y=-124x+8y=-24

Quiz Question #1

a) (6,-6)

b) (7,-1)

c) (-6,6)

The answer was (6,-6).Solution

-4x-2y=-124x+8y=-24

6y=-36 6 6

Y=-6

CORRECT !!!

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Add equations together

Divide by 6 on both sidesSolve for yStep Three

Step Two

Step One

Solution ContinuedY=-6

-4x-2(-6)=-12-4x+12=-12-12 -12

-4x=-24

X=6

Solution (6,-6)NEXT

Substitute for y to solve for x

Subtract 12 to both sides

Solve for xStep Six

Step Five

Step Four

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Q2: Solve the following problem using the substitution method.

2x-3y=-1Y=x-1

Quiz Question #2

a) (3,4)

b) (4,3)

c) (1,0)

The answer was (4,3).Solution2x-3y=-1

Y=x-12x-3(x-1)=-1

2x-3x+3=-1

CORRECT !!!

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Substitute for y

Step Two

Step One

Distribute the -3

Solution Continued-x=-4

X=4

Y=4-1

Y=3

Solution (4,3)

Step Three

Step Four

Divide both sides by -1

Step Five

Substitute for x in one equation to solve for y

Solve for y

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Q3: Which method would be easier to solve the following problem?

Y=-24x-3y=18

Quiz Question #3

a) Substitution

b) Elimination

c) Graphing

The answer was the substitution method.Solution

This method would work better because we already know what the y variable

equals.

CORRECT !!!

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Q4: Two small pitchers and one large pitcher can hold 8 cups of water.  One large pitcher minus one small pitcher constitutes 2 cups of water.  How many cups of  water can each pitcher hold?

Quiz Question #4

a) 3 small pitchers 4 large pitchers

b) 4 small pitchers 2 large pitchers

a) c) 2 small pitchers 4 large pitchers

The answer was the small pitcher(x) holds 2 cups and the larger pitcher(Y) holds 4 cups.

SolutionLet x= small pitcherLet y=large pitcher

2x+y=8-x+y=2

CORRECT !!!

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Step One Assign the variables

Step TwoExpress the problem as two equations

Solution Continued2x+y=8

-(-x+y=2)3x=6

X=2

2(2)+y=8

Y=4Solution( 2,4)

Step Three

Step Four

Subtract the two equations

Step Five

Solve for x

Plug x back into the equation

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Step Six Solve for y

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Q5: A test has twenty questions worth 100 points.  The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each.  How many multiple choice questions are on the test?

Quiz Question #5

a) 15

b) 5

c) 10

There are 5 multiple choice questions .Solution

Let x= T/F questionsLet y=Multiple Choice Questions

x+y=203x+11y=100

CORRECT !!!

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Step One

Step Two

Assign the variables

Express the problem as two equations

Solution Continued3(x+y=20)

3x+11y=100

3x+3y=60-(3x+11y=100)

-8y=-40Y=5

Step Three

Step Four

Multiply the first equation by 3

Step Five

Distribute the 3

Subtract the two equations

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Step Six Solve for y

Solution Continued

x+5=20

x= 15

Solution: 5 Multiple Choice Questions15 T/F Questions

Step Seven

Step Eight

Plug y back into the equation to solve for x

Solve for x

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You are an expert at solving systems of equations using the elimination and substitution method. Continue on with the great work!!!

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Congratulations!!!