7.5 S KM & PP 1

Systems of Equations

7.5 S KM & PP 2

Word Problem Basics

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

7.5 S KM & PP 3

Motion Problem Basics

d = distance

r = rate

t = time

7.5 S KM & PP 4

Motion Problem Basics

7.5 S KM & PP 5

Motion Problem Basics

50 50 1

100 50 2

150 50 3

200 50 4

7.5 S KM & PP 6

Take the Train!

A green train traveling at 42 mph

leaves the Roseville station

heading towards San Francisco.

Two hours later a red train, on a

parallel track, traveling at 70 mph

leaves Roseville heading towards

San Francisco. In how many hours

will the red train overtake the

green train?

7.5 S KM & PP 7

Take the Train!

Same distance!

7.5 S KM & PP 8

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.5 S KM & PP 9

Motion Problem Basics

d = distance

t = time

7.5 S KM & PP 10

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.5 S KM & PP 11

Take the Train!

d r t

d 42 t+2

d 70 t

Red

Green

7.5 S KM & PP 12

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.5 S KM & PP 13

Take the Train!

42(t 2) 70t

d 42(t 2) d 70t

42t 84 70t 84 28t

3 t

7.5 S KM & PP 14

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.5 S KM & PP 15

Take the Train!

A green train traveling at 52 mph

leaves the Roseville station

heading towards San Francisco.

Two hours later a red train, on a

parallel track, traveling at 70 mph

leaves Roseville heading towards

San Francisco. In how many hours

will the red train overtake the

green train?The red train will overtake the green

train in 3 hours.

7.5 S KM & PP 16

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.5 S KM & PP 17

Police!

Two police cars leave Roseville at

the same time, heading in

opposite directions. The first

police car is traveling at 25 mph

and the other police car is

traveling at 43 mph. In how many

hours will they be 136 miles apart?

7.5 S KM & PP 18

Identify Your Variables.

d = distance

t = time

7.5 S KM & PP 19

Police!

136 Miles

d 136- d

7.5 S KM & PP 20

d r t

d 25 t

136-d

43 tFirst

Second

Write a COMPLETE SYSTEM

7.5 S KM & PP 21

Algebraically SOLVE the SYSTEM

136 25t 43t 136 68t136

t68

2 t

t43d136

t25d

7.5 S KM & PP 22

Two police cars leave Roseville at

the same time, heading in

opposite directions. The first

police car is traveling at 25 mph

and the other police car is

traveling at 43 mph. In how many

hours will they be 136 miles apart?

Clearly answer the Question in Words

In 2 hours the cars will be 136 miles

apart.

7.5 S KM & PP 23

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.5 S KM & PP 24

Chickens!

At the same time, two chickens, 7

miles apart, head towards each

other.. The first chicken is

traveling at 5 mph and the other

chicken is traveling at 3 mph. In

how many hours will they meet?

7.5 S KM & PP 25

Identify Your Variables.

d = distance

t = time

7.5 S KM & PP 26

Chickens!

7 Miles

d 7 - d

7.5 S KM & PP 27

d r t

d 5 t

7 - d 3 t

First

Second

Write a COMPLETE SYSTEM

7.5 S KM & PP 28

Algebraically SOLVE the SYSTEM

7 5t 3t 7 8t

7t

8

t3d7

t5d

7.5 S KM & PP 29

At the same time two chickens, 7

miles apart, head towards each

other.. The first chicken is

traveling at 5 mph and the other

chicken is traveling at 3 mph. In

how many hours will they meet? The chickens will

meet in 7/8 hour

Clearly answer the Question in Words

7.5 S KM & PP 30

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.5 S KM & PP 31

That’s All for Now!