ALG  2A  LESSON  3:2    “USING  ALGEBRAIC  METHODS  TO  SOLVE  LINEAR  SYSTEMS”  -­‐  #15-­‐32,36,41,42  

NAME:  _____________________________    HR:____    SCORE:      _______    /21  

   

 

   

 

 

               

   

           

               

               

 

3-2 Using Algebraic Methods to Solve Linear Systems 195

For See Exercises Example

15–18 1 19–22 2 23–26 3 27 4

Independent Practice Classify each system and determine the number of solutions.

23. ! "

# 4y - x = -24

3x = 12y + 72

24. ! "

# 10x - 2y = 22

5y - 25x = 65

25. ! "

# 4y - 3x = 32

8y - 6x = 64

26. !

$

"

$

# -x + 3 _

4 y = 4

8x - 6y = -8

27. Business An office is printing 1200 copies of a document using two printers. During the process, printer A gets a paper jam and prints only half as many copies as printer B. Write and solve a system of equations to determine the number of copies each printer will produce.

Use substitution or elimination to solve each system of equations.

28.!"#

y + 3x = -21 x = 3y + 3

29.! " #

y = -2x + 14 1.5x - 3.5y = 2

30. ! $ " $

#

4 _ 5

y - 3x = 1 _ 5

y - x = 8

31. !

$

" $

#

x + 5y = 5 1 _ 5

x + 2y = -2

32. Exercise Ahmit gets exercise on the weekend by working around the house. On Saturday, he worked for 3 hours mowing the lawn and raking leaves. He burned 885 Calories. a. Write a system of

equations that can be used to describe the amount of time Ahmit worked and the number of Calories he burned by mowing and raking.

b. Determine how much time Ahmit spent on mowing and on raking.

33. Vanessa has collected $2.10 in dimes and nickels.a. Critical Thinking In how many different ways might Vanessa have

combined dimes and nickels to total $2.10?b. Critical Thinking How does the total number of coins change as the

number of dimes decreases? Explain.c. If Vanessa has exactly 30 coins, how many of each type of coin does she have?

34. /////ERROR ANALYSIS///// Two students attempted to solve the system of equations! " #

2x + 4y = 38 2x - 2y = -4

and found different answers. Which solution is incorrect?

Explain the error.

Raking leaves:275 Cal/h

Washing the car:240 Cal/h

Stacking firewood:350 Cal/h

Mowing the lawn:325 Cal/h

Skills Practice p. S8Application Practice p. S34

Extra Practice

a207se_c03l02_0190_0197.indd 195a207se_c03l02_0190_0197.indd 195 10/6/05 6:02:32 PM10/6/05 6:02:32 PM

 

   

3-2 Using Algebraic Methods to Solve Linear Systems 195

For See Exercises Example

15–18 1 19–22 2 23–26 3 27 4

Independent Practice Classify each system and determine the number of solutions.

23. ! "

# 4y - x = -24

3x = 12y + 72

24. ! "

# 10x - 2y = 22

5y - 25x = 65

25. ! "

# 4y - 3x = 32

8y - 6x = 64

26. ! $ "

$

# -x + 3 _

4 y = 4

8x - 6y = -8

27. Business An office is printing 1200 copies of a document using two printers. During the process, printer A gets a paper jam and prints only half as many copies as printer B. Write and solve a system of equations to determine the number of copies each printer will produce.

Use substitution or elimination to solve each system of equations.

28.!"#

y + 3x = -21 x = 3y + 3

29.! " #

y = -2x + 14 1.5x - 3.5y = 2

30. ! $ " $

#

4 _ 5

y - 3x = 1 _ 5

y - x = 8

31. ! $ " $

#

x + 5y = 5 1 _ 5

x + 2y = -2

32. Exercise Ahmit gets exercise on the weekend by working around the house. On Saturday, he worked for 3 hours mowing the lawn and raking leaves. He burned 885 Calories. a. Write a system of

equations that can be used to describe the amount of time Ahmit worked and the number of Calories he burned by mowing and raking.

b. Determine how much time Ahmit spent on mowing and on raking.

33. Vanessa has collected $2.10 in dimes and nickels.a. Critical Thinking In how many different ways might Vanessa have

combined dimes and nickels to total $2.10?b. Critical Thinking How does the total number of coins change as the

number of dimes decreases? Explain.c. If Vanessa has exactly 30 coins, how many of each type of coin does she have?

34. /////ERROR ANALYSIS///// Two students attempted to solve the system of equations! " #

2x + 4y = 38 2x - 2y = -4

and found different answers. Which solution is incorrect?

Explain the error.

Raking leaves:275 Cal/h

Washing the car:240 Cal/h

Stacking firewood:350 Cal/h

Mowing the lawn:325 Cal/h

Skills Practice p. S8Application Practice p. S34

Extra Practice

a207se_c03l02_0190_0197.indd 195a207se_c03l02_0190_0197.indd 195 10/6/05 6:02:32 PM10/6/05 6:02:32 PM