MS Algebra A-F-IF-7 Ch. 7.3a Solve Linear Systems by Elimination through Addition or Subtraction
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1 MS Algebra A-F-IF-7 Ch. 7.3a Solve Linear Systems by Elimination through Addition or Subtraction Mr. Deyo Solve Linear Systems by Elimination through Addition or Subtraction
2 Title: 7.3a Solve Linear Systems by Elimination with Addition/Subtraction Learning Target Date: By the end of the period, I will solve linear systems by elimination with addition or subtraction. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.
3 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 7.3 Pg ) Section TxtBk.Prob.#5,7,9,13,17,19 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due
4 Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1. How are the two images similar? 2. How are they different? 3. How can these two images be related to math?
5 Daily Warm-Up Exercises For use with pages xxx xxx One auto repair shop charges $30 for a diagnosis and $25 per hour for labor. Another auto repair shop charges $35 per hour for labor. For how many hours are the total charges for both of the shops the same?
6 Daily Warm-Up Exercises For use with pages xxx xxx One auto repair shop charges $30 for a diagnosis and $25 per hour for labor. Another auto repair shop charges $35 per hour for labor. For how many hours are the total charges for both of the shops the same? ANSWER 3 hours
7 Vocabulary 1) System of Linear Equations 2) Solution to a System of Equations 3) Solve by Graphing 4) Solve by Elimination 5) Solve by Substitution
8 Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example Word List Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing
9 Notes: Solving Systems by Elimination Step 1: Add or subtract the equations to eliminate one variable. Here we choose to ADD the two equations. Here we solve for x. Eq. 1: x y = 5 Eq. 2: + 3x + y = 3 4x = 8 Step 2: Solve the resulting equation for the other variable. 4x = x = 2 Step 3: Substitute in either original equation to find the value of the eliminated variable. Eq. 1: (2) y = 5 - y = 3 y = -3 Step 4: Check your solution Equation 1: 2 (-3) = 5 Equation 2: 3(2)+(-3)=3 Solution: (2,-3)
10 Problem A Use the Elimination method Solve the linear system. STEP 1 Add or Subtract the Equations STEP 2 Solve the resulting Equation for the Remaining Variable STEP 3 Substitute in either original equation to find the value of the eliminated variable. STEP 4 Check Solution STEP 3 2x + 3y = 11 Equation 1 +(-2x + 5y = 13) Equation 2 STEP 1 STEP 2 Solution: (, ) STEP 4
11 Problem A Use the Elimination method Solve the linear system. STEP 1 Add or Subtract the Equations STEP 2 Solve the resulting Equation for the Remaining Variable STEP 3 Substitute in either original equation to find the value of the eliminated variable. STEP 4 Check Solution 2x + 3y = 11 Equation 1 +(-2x + 5y = 13) Equation 2 8y = 24 y = 3 STEP 1 STEP 2 STEP 3 Solution: (1, 3) Equation 1 2x + 3(3) = 11 2x + 9 = x = x = 1 STEP 4 2(1) + 3(3) = = 11-2(1) + 5(3) = = 13
12 Problem B Use the Elimination method Solve the linear system. STEP 1 Add or Subtract the Equations STEP 2 Solve the resulting Equation for the Remaining Variable STEP 3 Substitute in either original equation to find the value of the eliminated variable. STEP 4 Check Solution 6x 4y = 14 Equation 1 STEP 3 +(-3x + 4y = 1) Equation 2 Solution: (, ) STEP 4
13 Problem B Use the Elimination method Solve the linear system. STEP 1 Add or Subtract the Equations STEP 2 Solve the resulting Equation for the Remaining Variable STEP 3 Substitute in either original equation to find the value of the eliminated variable. STEP 4 Check Solution 6x 4y = 14 Equation 1 +(-3x + 4y = 1) Equation 2 3x = x = 5 STEP 1 STEP 2 STEP 3 Solution: (5, 4) Equation 1 6(5) 4y = y = y = y = 4 STEP 4 6(5) 4(4) = = 14-3(5) + 4(4) = = 1
14 Storm Check (Think, Write, Discuss, Report) Explain in your own words the four steps of solving systems of equations by Elimination? The four steps of solving systems of equations by elimination are: 1) 2) 3) 4)
15 Problem A Use the Elimination method Solve the linear system. STEP 1 Add or Subtract the Equations STEP 2 Solve the resulting Equation for the Remaining Variable STEP 3 Substitute in either original equation to find the value of the eliminated variable. STEP 4 Check Solution - 4x + 3y = 2 Equation 1 (5x + 3y = -2) Equation 2 Solution: (, )
16 Problem A Use the Elimination method Solve the linear system. STEP 1 Add or Subtract the Equations STEP 2 Solve the resulting Equation for the Remaining Variable STEP 3 Substitute in either original equation to find the value of the eliminated variable. STEP 4 Check Solution - 4x + 3y = 2 Equation 1 (5x + 3y = -2) Equation 2 4x + 3y = 2-5x - 3y = +2) -1x = x = -4 STEP 1 STEP 2 STEP 3 Solution: (-4, 6) STEP 4 4(-4) + 3(6) = = 2 Equation 1 4(-4) + 3y = y = y = y = 6 5(-4) + 3(6) = = -2
17 Problem B Use the Elimination method Solve the linear system. STEP 1 Add or Subtract the Equations STEP 2 Solve the resulting Equation for the Remaining Variable STEP 3 Substitute in either original equation to find the value of the eliminated variable. STEP 4 Check Solution - 2x y = 7 Equation 1 (2x + 7y = 31) Equation 2 Solution: (, )
18 Problem B Use the Elimination method Solve the linear system. STEP 1 Add or Subtract the Equations STEP 2 Solve the resulting Equation for the Remaining Variable STEP 3 Substitute in either original equation to find the value of the eliminated variable. STEP 4 Check Solution - 2x y = 7 Equation 1 (2x + 7y = 31) Equation 2 2x y = 7-2x 7y = -31) -8y = y = 3 STEP 1 STEP 2 STEP 3 Solution: (5, 3) STEP 4 2(5) (3) = = 7 Equation 1 2x (3) = 7 2x 3 = x = x = 5 2(5) + 7(3) = = 31
19 Storm Check (Think, Write, Discuss, Report) To verify your solution to a system of linear equations, what do you have to do? To verify my solution to a system of linear equations, I have to.
20 Vocabulary 1) System of Linear Equations 2) Solution to a System of Equations 3) Solve by Graphing 4) Solve by Elimination 5) Solve by Substitution
21 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 7.3 Pg ) Section TxtBk.Prob.#5,7,9,13,17,19 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due
22 Title: 7.2 Solve Linear Systems by Substitution Date: Learning Target By the end of the period, I will solve linear systems by substitution. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.
23 Ticket Out Solve the System of Equations: Eq. 1: x y = 5 Eq. 2: 3x + y = 3
24 2 y = 5 -y = 3 y = -3 Ticket Out Solve the System of Equations: Eq. 1: x y = 5 Eq. 2: 3x + y = 3 Solution: (2,-3) 4x = 8 x = 2
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