Systems of Equations By: China King NEXT

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 In the elimination method you add or subtract the equations to get an equation in one variable. Example 3y+2x=6 5y-2x=10 Elimination We can eliminate the x-variable by adding the two equations together STEP 1 NEXT HOME BACK

 We can now solve for the y- variable. Example 3y+2x=6 + 5y-2x=10 8y=16 Elimination STEP 2 NEXT HOME BACK

 We can divide both sides of the equation by 8. Example 8y=168 Y=2 Elimination STEP 3 NEXT HOME BACK

 Now that we know that y=2. We substitute that answer into the other equation to solve for the x- variable. Example 3y+2x=6 3(2)+2x=6 6+2x=6 Elimination STEP 4 NEXT HOME BACK

 Subtract 6 from both sides. Example 6+2x=6 -6 2x=0 Elimination STEP 5 NEXT HOME BACK

 Divide by -2 on both sides Example 2x=02 X=0 Elimination STEP 6 NEXT HOME BACK

Example 3y+2x=6 + 5y-2x=10 The solution to the following problem is X=0 Y=2 (0,2) Elimination NEXT HOME BACK

Elimination NEXT HOME Double Click for video to play

Q1: What was the first step in the elimination process? Quick Check #1 HOME a)Multiply by 2Multiply 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. NEXT

 That’s not correct. Lets watch the video again. NEXT

Video #2 NEXT HOME Double Click for video to play

Q1: What was the last step in the elimination process? Quick Check #2 HOME BACK a)Check your answerCheck 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. NEXT

 That’s not correct. Lets watch the video again. NEXT

Q3: Solve the following system of equation. x+2y=4 3x+y=2 Quick Check #3 HOME a)(2,0)(2,0)b) (1,-1)c) (0,2)

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

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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 NEXT HOME

Substitution NEXT HOME BACK Double Click for video to play

Q1: What was the first step in the substitution process? Quick Check #1 HOME BACK a)Substitute for xSubstitute 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. NEXT

 That’s not correct. Lets watch the video again. NEXT

Substitution NEXT HOME

Q1: What was the last step in the substitution process? Quick Check #2 HOME a)Multiply by 2Multiply 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. NEXT

 That’s not correct. Lets watch the video again. NEXT

Q3: Solve the following system of equation by using substitution. X-2y=-10 Y=3x Quick Check #3 a)(6,2)(6,2)c) (0,0)b) (2,6)

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

 That’s not correct. Let’s try doing the problem again. NEXT

Start Quiz

Q1: Solve the following problem using the elimination method. -4x-2y=-12 4x+8y=-24 Quiz Question #1 a)(6,-6)(6,-6)b) (7,-1)c) (-6,6)

 The answer was (6,-6). Solution -4x-2y=-12 4x+8y=-24 6y= Y=-6 NEXT Add equations together Divide by 6 on both sides Solve for y Step Three Step Two Step One

Solution Continued Y=-6 -4x-2(-6)=-12 -4x+12= x=-24 X=6 Solution (6,-6) NEXT Substitute for y to solve for x Subtract 12 to both sides Solve for x Step Six Step Five Step Four

 That’s not correct. Let’s try doing the problem again. NEXT

Q2: Solve the following problem using the substitution method. 2x-3y=-1 Y=x-1 Quiz Question #2 a)(3,4)(3,4)b) (4,3)c) (1,0)

 The answer was (4,3). Solution 2x-3y=-1 Y=x-1 2x-3(x-1)=-1 2x-3x+3=-1 NEXT 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 NEXT

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Q3: Which method would be easier to solve the following problem? Y=-2 4x-3y=18 Quiz Question #3 a)SubstitutionSubstitution 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. NEXT

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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 pitchers3 small pitchers 4 large pitchers b) 4 small pitchers 2 large pitchers a)c) 2 small pitchersc) 2 small pitchers 4 large pitchers

 The answer was the small pitcher(x) holds 2 cups and the larger pitcher(Y) holds 4 cups. Solution Let x= small pitcher Let y=large pitcher 2x+y=8 -x+y=2 NEXT Step One Assign the variables Step Two Express the problem as two equations

Solution Continued 2x+y=8 -(-x+y=2) 3x=6 X=2 2(2)+y=8 Y=4 Solution( 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)1515 b) 5 c) 10

 There are 5 multiple choice questions. Solution Let x= T/F questions Let y=Multiple Choice Questions x+y=20 3x+11y=100 NEXT Step One Step Two Assign the variables Express the problem as two equations

Solution Continued 3(x+y=20) 3x+11y=100 3x+3y=60 -(3x+11y=100) -8y=-40 Y=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 Questions 15 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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 You are an expert at solving systems of equations using the elimination and substitution method. Continue on with the great work!!! NEXT