Core Connections Algebra Chapter 4: Systems of Equations. Team number How can I use variables to solve problems?

Transcription

1 Core Connections Algebra Chapter 4: Systems of Equations Name Team number How can I use variables to solve problems? Solving Word Problems by Writing Equations 4-1. Mathematical Sentences: Translations: 1. A zoo has two fewer elephants than zebras and five times more monkeys than elephants. The total number of elephants, monkeys, and zebras is Zola earned $30 by working two hours and receiving a $12 bonus. 3. Thirty ounces of metal is created by mixing zinc with silver. The number of ounces of silver needed is twelve times the number of ounces of zinc. 4. Eddie, who earns $5 per hour, worked two hours longer than Zach, who earns $12 per hour. Together they earned $ b.) c.) d.) 4-3. a.) What is missing? b.) Mathematical Sentence: Side #2: Side #3: c.) Side #1: Side #2: Side #3:

2 4-4. THE ENVIRONMENTAL CLUB Tables: x represents: y represents: Amy s Tree: x y Charlie s Tree: x y Equations: Graph: Work: Amy s Tree: Charlie s Tree: 4-5. Amy s Tree: Domain: Range: Charlie s Tree: Domain: Range: y-intercepts: What does the y-intercept represent?

3 4-6. a.) Let Statement: Equation(s): b.) Let Statement: Equation(s): c.) Let Statement: Equation(s): 4-7. Solve: In how many months would they have the same amount of savings? How much savings would they have at that time? Closure: How many equations do I need? One Equation or Two? ONE EQUATION OR TWO? a. Solomon s Equation: 12b: 10(4b + 1): 218: b. Marcus Equations: c: 4b + 1: 12b: 10c: 218:

4 c. d. Solution: a.) b.) Change the equation(s): Equation 1: Equation 2: c.) Solve: d.) Change to y= form: Solve the System of Equations:

5 4-23. Solve: Equation 1: Equation 2: Solve: Closure: Equal Values Method How can I solve the system? Solving Systems of Equations Using Substitution Solve:

6 4-32. AVOIDING THE MESS a.) b.) c.) Solve the equation: Plug in your answer for x to solve for y: y = -x-7 5y + 3x = a.) y=3x 2y-5x=4 b.) x-4=y -5y+8x=29 x y c.) 2x+2y=18 x=3-y x y d.) c=-b-11 3c+6=6b x y x y 4-34.

7 4-35. HAPPY BIRTHDAY! Equation(s): Solve: Closure: Substitution Method How does a graph show a solution? Making Connections: Systems, Solutions and Graphs 4-42 through THE HILLS ARE ALIVE Equation #1: Let x = and y =. x y Equation #2: x y

8 Solve the system by substitution: 40 Graph: a.) Solve: b.) 2x+2y=18 c. and d.) x y e.) 4-47.

9 a.) 10x 4y 8 x y Graph: y 5 2 x 2 10x 4y 8 y 5 2 x b) Prediction: Closure: What is a solution to a two-variable equation? Can I solve without substituting? Solving Systems Using Elimination 4-55.

10 4-56. Parts a b and c use Algebra Tiles d) Solve for x: e.) Use the solution to solve for y. Check both equations. f.) Solve using the elimination method: 2x-y=-2-2x+3y= a.) Write a system of equations: b.) Good candidate for Elimination Method? Why or why not? c.) Solve:

11 4-58. Solve: 2 x 7 y 13 2x 3y a. 2y x 5 3y x 9 b. 2x 4y 14 4y x 3 c. 3x 4y 1 2x 4y 2 Closure: Elimination Method

12 4.2.4 How can I eliminate a variable? More Elimination Which system? Solve: a.) b.) c.) d.) a.) Elimination Method? 5m 2n 10 3m 2n 2 Why or Why Not? Solution: ( m, n ) = (, )

13 b.) Elimination Method? 6a b 3 b 4a 17 Why or Why Not? Solution: ( a, b ) = (, ) c.) Elimination Method? 7x 4y 17 3x 2y 15 Why or Why Not? Solution: ( x, y ) = (, ) Combine and Solve: Are they the same line? How can you tell? What does this mean?

14 4-70. Solve: Closure: For what kind of systems is elimination the best strategy? How do you know if you need to change one equation or both before combining equations? What s the point of using the elimination method? What happens if both variables are eliminated when you combine two equations?

15 4.2.5 What is the best method? Choosing a Strategy for Solving Systems a.) b.) Substitution: Elimination: a.) Which method? b.) Which method? c.) Which method? d.) Which method? e.) Which method? f.) Which method? g.) Which method? h.) Which method? Problems will be assigned by your teacher

16 System #1: Solution: (, ) System #2: Solution: (, ) System #3: Solution: (, )

17 System #4: Solution: (, ) Closure: Solving Systems of Equations

18 4.3.1 What can I do now? Pulling It All Together a.) Graph: 35 b.) c.) Write the System: Solve: 4-89.

19 Area as a sum: Area as a product: a.) TeleTalk: AmeriCall: CellTime: Which company should she use?: b.) TeleTalk: AmeriCall: CellTime: Rule: Rule: Rule: x y x y x y c.) d.)

20 Graph: a.) b.) a.) b.)

21 c.) d.) a.) b.) Legal? Why or why not? a.) Legal? Why or why not? b.) Legal? Why or why not? c.) Legal? Why or why not? d.) Legal? Why or why not?

22 4-96. Method #1: Method #2: Solve using Substitution: y=x 2 +5 y=x 2 +2x+1