HW: pgs. 256-257 #11-27odd, 28-31

         

         

         

         

         

           

           

           

           

           

           

           

           

Weeks

Mo

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y S

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d ($

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28. y = 5x + 2528. y = 8x + 1629. Answer: 3 weeks

1 2 3 4 5

30. y = 15x + 1028. y = -20x + 15029. Answer: 4 minutes

He

igh

t (m

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Minutes

605040302010

16014012010080604020

1 2 3 4 5

Substitution: a method to solve a system of equations.

A. Use substitution to solve the system of equations.x = 4y4x – y = 75

Answer: (20, 5)

5-2 Substitution

Step 1: Since x = 4y, substitute 4y for x in the 2nd equation.

4(4y) – y = 75

16y – y

=

75

15y

=

75

y = 5

Step 2: Use x = 4y to find the value of x.

x = 4y

x = 4(5)

x = 20

B. Use substitution to solve the system of equations.4x + y = 12–2x – 3y = 14

Answer: (5, -8)

First, solve the first equation for y since the coefficient of y is 1. 4x + y = 12 y = -4x + 12

Then find the value of x by substituting -4x + 12 for y in the second equation.

–2x – 3y

=

14

–2x – 3(-4x+12)

=

14

–2x +12x – 36

=

14

10x – 36

=

14

10x

=

50

x = 5

Lastly, substitute 5 for x in either equation to find the value of y.

y = -4x + 12

y = -4(5) + 12

y = -20 + 12

y = –8

Use substitution to solve the system of equations.A. 2a + 2b = 8 a + b = –2

Answer: No solution

B. 6x – 2y = -4 y = 3x + 2

Answer: Infinitely many

a = -b – 2

2(-b – 2) + 2b = 8

-2b – 4 + 2b = 8

-4 = 8

6x – 2(3x + 2) = -4

6x – 6x – 4 = -4

-4 = -4

1. A

2. B

3. C

4. D

Answer: 2 mL of 10% HCl solution, 8 mL of 40% HCl solution

CHEMISTRY Michael needs 10 milliliters of 34% HCl (hydrochloric acid) solution for a chemistry experiment. There is a bottle of 10% HCl solution and a bottle of 40% HCl solution in the lab. How much of each solution should he use to obtain the required amount of 34% HCl solution? (Think back to chapter 2… this time we will use 2 equations instead)

Given information

10 mL 34% HCL

x mL 10% HCL

y mL 40% HCL

System of Equations

x + y = 10

0.10x + 0.40y = 0.34(10)

Solve

y = 10 – x

0.10x + 0.40(10 – x) = 3.4

0.1x + 4 – 0.4x = 3.4

-0.3x = -6

x = 2

y = 10 – x

y = 10 – 2

y = 8

1. A

2. B

3. C

4. D

Amy and Rachel are both saving money for a summer vacation. Amy has already saved $100 and plans to save $25 per week until the trip. Rachel has $75 and plans to save $30 per week. In how many weeks will they have the same amount of money? Graph the system of equations to find the answer. (Hint: Go by 25 for the y scale).

Use may use Graphing calculator:

1. Enter equations in y=

2. 2nd [Calc] 5 Enter Enter EnterAnswer: 5 weeks

12-9 Honors Algebra Warm-up