1. { { { { WARM-UP Date: 3/10/09 Solve the system. 12x + 4y = -8
Solve by graphing. 2.
Solve the system. { 1.
12x + 4y = -8
y = x + 2 {
3x + 4y = x + 9y = 1 3.
Solve the system. 4.
Solve the system. {
-3x = -2y – 37
x = 2y + 19 {
4x – 2y = -10
y = 2x + 5

2. { 15x + 20y = 10 1. Solve the system. + -15x – 27y = -3 -7y = 7 -7 -7
= 10
1. Solve the system. +
-15x
– 27y
= -3
-7y
= 7 -7 -7 {
5( )
y = -1
3x + 4y = x + 9y = 1
-3( )
3x + 4y = 2
3x + 4 (-1) = 2
3x – 4 = 2 +4 +4 3x
= 6 3 3
x = 2
Solution (1, -1)

3. 2. Find the solution to the systems by graphing.
12x + 4y = -8
-12x
-12x
y = x + 2
2. Find the solution to the systems by graphing.
4y =
-8 – 12x 4 4
y = -2 – 3x {
12x + 4y = -8
y = x + 2
Solution (-1, 2)

4. { Substitute the x: -3(2y + 19) = -2y – 37
3. Use substitution to solve systems.
-6y
– =
-2y – 37
+2y
+2y
-4y
– =
-37 {
-3x = -2y – 37
x = 2y + 19
+57
+57
-4y = 20 -4 -4
y = -5
x = 2y + 19
Substitute the y:
x = 2(-5) + 19
x = 9
x, y
Solution: (9, -5)

5. { 4x – 2(2x + 5) = -10 Solve by substitution. 4x – 4x – 10 = -104.
Solve by substitution. 4x
– 4x
– 10
= -10 {
4x – 2y = -10
y = 2x + 5 0x
– 10 = -10
-10
= -10
Is this a true?
YES
Infinite Solutions

6. Solving Word Problems with Systems
Name: Pd
Algebra /10/09

7. Word Problem Steps Figure out what the question is.
Determine what the variables need to be.
Find key numbers.
Create Equations.
Solve.

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

9. f:
Ex2: Rob bought 15 concert tickets worth $ 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.
# of floor seats b:
# of balcony seats {
25f b =
f + b = 15

10. d:
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.
# of dime q:
# of quarter {
0.10d q = 3.35
d + q = 14

11. c:
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.
# of country CDs r:
# of rock CDs {
c = 3r – 7
r + c = 78

12. Ex5: Fred went to the fruit stand to purchase oranges and bananas
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 $ What is the cost of each orange and banana? R:
Cost of a orange B:
Cost of a banana {
7( )
5R + 6B = 2.05
-5( )
7R + 8B = 2.79
35R
+ 42B
= 14.35 +
-35R
– 40B = 2B = 2 2
B = 0.2
Bananas $0.20.

13. Ex5: Fred went to the fruit stand to purchase oranges and bananas
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 $ What is the cost of each orange and banana?
B = 0.2
5R + 6B = 2.05
5R + 6(0.2) = 2.05
5R +1.2 = 2.05
-1.2
-1.2 5R
= 0.85 5 5
R = 0.17
Oranges $0.17

14. Ex6: At a small town baseball game there were 78 people
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:
Number of adults b:
Number of children {
7a + 2c = 421
-2( )
a + c = 78
7a + 2c = 421
-2a
– 2c
= -156 + 5a
= 265 5 5
a = 53
53 adults

15. { R: # hours Rachel worked
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? B:
# hours Bob worked {
R = B – 4
R + B = 38
B – 4
+ B
= 38 2B
– 4 = 38
+ 4 +4 2B
= 44 2 2
B = 22
Bob worked 22 hours.

16. Ex7: Rachel and Bob work as part-time employees for a lawyer
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?
B = 22
R = B – 4
R = 22 – 4
R = 18
Rachel worked 18 hours.

17. { L: length of a rectangle
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)? W:
width of a rectangle {
L = 3w – 4
2W + 2L = 48
2w + 2(3w – 4) = 48 2w
+ 6w
– 8
= 48 8w
– 8 = 48
+ 8 +8 8w
= 56 8 8
w = 7
Width 7 meters.

18. 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)?
w = 7
L = 3(7) – 4
L = 21 – 4
L = 17
Length is 17 m.

19. 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.