Page 195 - Math Course 2 (Book 1)

Solving Systems of Equations by Multiplying

Write and Solve a System of
MO. 6 - L4b
Equations
Problem-Solving Using

Elimination by Multiplying Example

TRANSPORTATION
Let’s Begin A f shing boat travels 10 miles downstream in 30

minutes. The return trip takes the boat 40 minutes.
Find the rate of the boat in still water.

Writing Systems of Equations Let b = the rate of the boat in still water.

Let c = the rate of the current.
Example Use the formula rate • time = distance, or rt = d.

Since the rate is miles per hour, write 30 minutes as
1 2
John has 30 science-f ction and hour and 40 minutes as hour.
3
2
mystery books. Four times the number of science
f ction books minus the number of mystery books r t d rt = d
is 5. Which system of equations can be used to f nd
how many science f ction, f, and mystery, m, books
1
he has? Down- b + c 1 10 1 b + c = 10
stream 2 2 2
A. f + m = 30 B. f + m = 30
f – 4m = 5 4f – m = 5 Up- 2 2 2
stream b – c 3 10 3 b – c = 10
3
C. f + m = 30 D. f + m = 30
f + 4m = 5 4f + m = 5
Read the Test Item Use elimination with multiplication to solve this
You are asked to f nd a system of equations to system. Since the problem asks for b, eliminate c.
represent this situation using f, the number of
science f ction books and m, the number of 1 1 2 2 20 2
mysteries. b + c = 10 b + c = 3 Multiply 3
2
2
6
6
(+)
Solve the Test Item
2
2
2
2
Represent the situation algebraically by writing two b – c = 10 b – c = 5 Multiply 1
equations. The total number of science f ction and 3 3 6 6 2
mystery books is 30.
4 35 Add the
b =
f + m = 30 One equation is f + m = 30. 6 3 equations
Four times the number of science f ction books 6 4 6 35 Multiply each
minus the number of mystery books is 5. 4 b = 4 3 side by 6
6
4
4f – m = 5 The second equation is 4f – m = 5. 70
b = or 17.5 Simplify.
4
The system of equations that
represents this situation is
Answer Answer The rate of the boat is 17.5 mph
f + m = 30 and 4f – m = 5.
The answer is B.

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