WARM-UP Date: 3/10/09

1.

4.

3. Solve the system.

Solve the system. 2. Solve by graphing.

4x – 2y = -10y = 2x + 5 {

3x + 4y = 2 5x + 9y = 1

{Solve the system.

12x + 4y = -8y = x + 2{

-3x = -2y – 37 x = 2y + 19

{

5( )

+ 20y

{ 3x + 4y = 2 5x + 9y = 1

15x-15x+

-7y = 7-7 -7

y = -1 3x + 4y = 2

3x + 4 (-1) = 2 3x – 4 = 2

+4 +4 3x = 63 3

x = 2

1. Solve the system.

Solution (1, -1)

= 10

-3( )

– 27y = -3

2. Find the solution to the systems by graphing.

12x + 4y = -8y = x + 2{

12x + 4y = -8-12x -12x

4y = -8 – 12x 4 4y = -2 – 3x

y = x + 2

Solution (-1, 2)

-3x = -2y – 37 x = 2y + 19{

-3(2y + 19) = -2y – 37 -6y – 57 = -2y – 37

+2y+2y-4y – 57 = -37

+57 +57 -4y = 20

-4 -4 y = -5

x = 2y + 19 x = 2(-5) + 19 x = 9

3. Use substitution to solve systems.

Substitute the x:

Substitute the y:

Solution: (9, -5) x, y

4. Solve by substitution. 4x – 2(2x + 5) = -10

4x – 2y = -10y = 2x + 5 {

4x – 4x – 10 0x – 10 = -10

-10 = -10

Is this a true?

= -10

YES

Infinite Solutions

Solving Word Problems with Systems

Name: Pd

Algebra 3/10/09

Word Problem Steps

1. Figure out what the question is.

2. Determine what the variables need to be.

3. Find key numbers.

4. Create Equations.

5. Solve.

Ex1: Paula went to get school supplies. If she buys 8 pencils and 5 notebooks it will cost $8.30. If she buys 12 pencils and 3 notebooks it will cost $5.70. Write a system describing the cost of a pencil, p, and notebook, n.

12p + 3n = 5.70{

p:cost of pencilsn:cost of notebooks

8p + 5n = 8.30

Ex2: Rob bought 15 concert tickets worth $322.50. Floor tickets cost $25 each while the balcony tickets cost $17.50 each. Write a system for the number of balcony seats, b and floor seats, f, purchased.

f + b = 15{

f: # of floor seatsb:# of balcony seats

25f + 17.50b = 322.50

Ex3: Micah has a total of $3.35 in dimes and quarters. If he has 14 coins, write an equation for finding the number of dimes, d, and quarters, q.

d + q = 14{

d:# of dimeq:# of quarter

0.10d + 0.25q = 3.35

Ex4: Jamie has 78 rock and country CDs in his collection. The number of country CDs he has is 7 less than 3 times the number of rock CDs he has. Write a system for finding the number of rock, r, and c, country CDs he has.

r + c = 78 {

c: # of country CDsr:# of rock CDs

c = 3r – 7

{ 7( )

Ex5: Fred went to the fruit stand to purchase oranges and bananas. He can purchase 5 oranges and 6 bananas for $2.05 or he can purchase 7 oranges and 8 bananas for $2.79. What is the cost of each orange and banana?

7R + 8B = 2.79

R: Cost of a orange

B: Cost of a banana

5R + 6B = 2.05

-5( )

-35R – 40B = -13.95+

2B = 0.40

2 2

B = 0.2

35R + 42B = 14.35

Bananas $0.20.

5R + 6B = 2.05

5R + 6(0.2) = 2.05

5R +1.2 = 2.05

B = 0.2

-1.2 -1.2

5R = 0.85

5 5

R = 0.17

Oranges $0.17

Ex5: Fred went to the fruit stand to purchase oranges and bananas. He can purchase 5 oranges and 6 bananas for $2.05 or he can purchase 7 oranges and 8 bananas for $2.79. What is the cost of each orange and banana?

-2( )

Ex6: At a small town baseball game there were 78 people. Children tickets were $2 and adult tickets were $7. If $421 was made at the game, how many adults went?

a + c = 78{

a: Number of adultsb: Number of children

7a + 2c = 421

-2a – 2c = -156 7a + 2c = 421

+

5a = 265

5 5

a = 53

53 adults

2B

B – 4

Ex7: Rachel and Bob work as part-time employees for a lawyer. Last weeks Rachel worked 4 hours less than Bob worked. Together they worked 38 hours total. How many hours did Bob and Rachel work?

R + B = 38{R: # hours Rachel worked

B: # hours Bob workedR = B – 4

+ B

– 4 = 38 + 4 +4

2B = 44 2 2

B = 22

= 38

Bob worked 22 hours.

R = B – 4

R = 22 – 4

R = 18

B = 22

Rachel worked 18 hours.

Ex7: Rachel and Bob work as part-time employees for a lawyer. Last weeks Rachel worked 4 hours less than Bob worked. Together they worked 38 hours total. How many hours did Bob and Rachel work?

8w

+ 6w

Ex8: The length of a rectangle is 4 meters less than three times its width. If the perimeter of the rectangle is 48 meters, then what is the value of the length (in meters)?

2W + 2L = 48{

L: length of a rectangle

W: width of a rectangle

L = 3w – 4

2w + 2(3w – 4) = 482w – 8

– 8 = 48 + 8 +8

8w = 56 8 8

w = 7

= 48

Width 7 meters.

L = 3(7) – 4

L = 21 – 4

L = 17

w = 7

Length is 17 m.

Ex8: The length of a rectangle is 4 meters less than three times its width. If the perimeter of the rectangle is 48 meters, then what is the value of the length (in meters)?

• Complete your practice packets to be turned in at the end of class

• If you finish early please begin your exit ticket and begin your homework.