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Systems of EquationsBy: China King
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Directions
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Home
ELIMINATION METHOD
SUBSITUTION METHOD
QUIZ
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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
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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
NEXTHOMEBACK
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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
NEXTHOME
Double Click for video to play
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Q1: What was the first step in the elimination process?
Quick Check #1
HOME
a) Multiply by 2
b) Add the equations together
c) Subtract the two equations
d) I have no clue
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The first step in the elimination process was to add the two equations together.
CORRECT !!!
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That’s not correct. Lets watch the video again.
SORRY
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Video #2
NEXTHOME
Double Click for video to play
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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
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The last step in the elimination process was to check your answer.
CORRECT !!!
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That’s not correct. Lets watch the video again.
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)
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The answer is (0,2). You are a master of the elimination method!!!
CORRECT !!!
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That’s not correct. Let’s try doing the problem again.
SORRY
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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
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Substitution
NEXTHOMEBACK
Double Click for video to play
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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
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The first step in the substitution process was to substitute for x.
CORRECT !!!
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That’s not correct. Lets watch the video again.
SORRY
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Substitution
NEXTHOME
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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
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The last step in the substitution process was to check your answer.
CORRECT !!!
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That’s not correct. Lets watch the video again.
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)
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The answer is (2,6). You are a master of the substitution method!!!
CORRECT !!!
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That’s not correct. Let’s try doing the problem again.
SORRY
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Start Quiz
Quiz
Time!
Quiz Time!Quiz Time!
Quiz Time!
QUIZ TIME!
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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)
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The answer was (6,-6).Solution
-4x-2y=-124x+8y=-24
6y=-36 6 6
Y=-6
CORRECT !!!
NEXT
Add equations together
Divide by 6 on both sidesSolve for yStep Three
Step Two
Step One
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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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That’s not correct. Let’s try doing the problem again.
SORRY
NEXT
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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)
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The answer was (4,3).Solution2x-3y=-1
Y=x-12x-3(x-1)=-1
2x-3x+3=-1
CORRECT !!!
NEXT
Substitute for y
Step Two
Step One
Distribute the -3
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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
NEXT
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That’s not correct. Let’s try doing the problem again.
SORRY
NEXT
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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
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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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That’s not correct. Let’s try answering the question again.
SORRY
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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
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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
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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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That’s not correct. Let’s try doing the problem again.
SORRY
NEXT
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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
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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
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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
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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
NEXT
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That’s not correct. Let’s try doing the problem again.
SORRY
NEXT
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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!!!
NEXT
Congratulations!!!