Algebra 24.2, 4.3a

Machhapuchhare

SAT Question: When it is 7:00 am in Seattle, it is 10:00 am in Philadelphia. A plane is scheduled to leave Philadelphia at 11:30 am (Philadelphia time) and to arrive in Seattle at 4:15 pm (Seattle time). How many hours are scheduled for the trip?

34

43

541

64

17

4

37

4

A.

B.

C.

D.

E.

11:30 to 4:15 is 4 ¾ hours.Add three hours for the time change.E is the answer.

2 6

3 4 4

x y

x y

The substitution method is best to use when one equation is solved for one of the variables, or when one equation has a variable with a coefficient of 1.

3 4 4

3 4( 2 6) 4

x y

x x

1 2 6y x

3 8 24 4x x 5 24 4x

5 20x 4x

2(4) 6

8 6

2

y

y

y

(4, 2)

2 1

3 2 12

y x

y x

3 2 12

3 2( 2 1) 12

y x

y y

1 2 1x y

3 4 2 12y y 7 2 12y

7 14y 2y

2 1

2(2) 1

3

x y

x

x

( 3,2)

Example 2

5 3 6

1

x y

x y

5 3 6

5( 1) 3 6

x y

y y

1 1x y

5 5 3 6y y 8 5 6y

8 11y 11

8y

1

111

83

8

x y

x

x

3 11,

8 8

Example 3

The linear combination method works best when both equations are in the form Ax + By = C, and especially when

none of the variables have a coefficient of 1.We use the properties of addition and multiplication to solve

using linear combinations.

Steps:1. Write both equations in the form Ax + By = C2. Clear fractions or decimals.3. Choose a variable to eliminate.4. Eliminate the variable by multiplying by an appropriate

number to make the two variables add to zero; then add the equations together.

5. Check by substituting answer into original equations.

3 4 1

3 2 0

x y

x y

Example 1:

3 4 1

3 2 0

x y

x y

2 1y 1

2y

3 4 1

13 4 1

2

x y

x

3 2 1x 3 1x

1

3x

1 1,

3 2

Example 2:

6 6 30

2 6 22

x y

x y

4 8x

3 3 15

3(2) 3 15

x y

y

6 3 15y 3 9y

3y

2,3

2) 3 3 15

2 6 22

x y

x y

3 3 15

2 6 22

x y

x y

2x

Example 3:

1

1

y

y

6 2 16

6 2(1) 16

x y

x

6 2 16x

6 18x 3x

6 2 16

12 5 31

x y

x y

2) 6 2 16

12 5 31

x y

x y

12 4 32

12 5 31

x y

x y

3,1

Example 4:

37 37

1

x

x

5 4 11

5( 1) 4 11

x y

y

5 4 11y 4 16y

4y

1,4

25 20 55

12 20 92

x y

x y

5 4 11

3 5 23

x y

x y

5) 5 4 11

4) 3 5 23

x y

x y

Example 5: 3 5 1

3 5(1) 1

x y

x

3 5 1x 3 6x

2x

2,1

0.3 0.5 0.1

0.01 0.4 0.38

x y

x y

3 5 1

40 38

x y

x y

3 5 1

3 120 114

x y

x y

115 115

1

y

y

10)

100)

0.3 0.5 0.1

0.01 0.4 0.38

x y

x y

3)

Example 5: 3 4 6

9 4 24

x y

x y

12 30x 5

2x

53 4 6

2

154 6

215

4 6(2) ( )2

2 (2)

y

y

y

1 21

2 33 1

24 3

x y

x y

1 21

2 33 1

24

(6) (6) (6)

(12) (12) )3

(12

x y

x y

3 2

3 4

15 8 12y

15 8 12y 5

2x

8 3y

3

8y

5 3,

2 8

Example of simple word problem: Eight small boxes plus 5 large boxes cost $184. A large box costs $3.00 more than a small box. What is the cost of each size of box?

x = small boxy = large box

8 5 184

3

x y

y x

8 5(3 ) 184x x 8 15 5 184x x

13 169x 13x

3 13

16

y

y

$13 for small box; $16 for large box

Classwork: 2, 10, 14, 18, 22/166;

2/171

Get ready for a “Small Quiz” to be written

on your grade sheet.

THE END

Quiz. Copy the problems and write the answer.

Put your grade paper on the front of your row, quiz side down.

Find the solution by graphing:

3 2 4

2 5

x y

x y