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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
NEXTHOMEBACK
We can now solve for the y- variable.Example3y+2x=6
+ 5y-2x=108y=16
Elimination
STEP 2
NEXTHOMEBACK
We can divide both sides of the equation by 8.
Example8y=168 8Y=2
Elimination
STEP 3
NEXTHOMEBACK
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
NEXTHOMEBACK
Subtract 6 from both sides.Example6+2x=6-6 -6
2x=0
Elimination
STEP 5
NEXTHOMEBACK
Divide by -2 on both sidesExample
2x=02 2 X=0
Elimination
STEP 6
NEXTHOMEBACK
Example3y+2x=6
+ 5y-2x=10
The solution to the following problem isX=0 Y=2
(0,2)
Elimination
NEXTHOMEBACK
Elimination
NEXTHOME
Double Click for video to play
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
NEXTHOME
Double Click for video to play
Q1: What was the last step in the elimination process?
Quick Check #2
HOMEBACK
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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SORRY
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Q3: Solve the following system of equation.x+2y=43x+y=2
Quick Check #3
HOME
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
NEXTHOME
Substitution
NEXTHOMEBACK
Double Click for video to play
Q1: What was the first step in the substitution process?
Quick Check #1
HOMEBACK
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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SORRY
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Substitution
NEXTHOME
Q1: What was the last step in the substitution process?
Quick Check #2
HOME
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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SORRY
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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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SORRY
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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
NEXT
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 !!!
NEXTNEXT
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
NEXT
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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SORRY
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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!!!