Download BENCHMARK 2 C. Rewriting Equations in Two or More

Name ———————————————————————
Date ————————————
BENCHMARK 2
(Chapters 3 and 4)
C. Rewriting Equations in Two or More
Variables (pp. 27–28)
A literal equation describes the relationship between two or more variables. The
equation can be rewritten, or “solved,” to isolate any one of the variables. The following
examples show how to solve and use literal equations.
1. Solve a Literal Equation
Vocabulary
Solve y mx b for m.
Solution:
Remember that
inverse operations
apply to variables
as well as to
constants.
PRACTICE
y 5 mx 1 b
Write original equation.
y 2 b 5 mx
Subtract b from each side.
y2b
}
x 5m
Assume x q 0. Divide each side by x.
Solve the literal equation for the specified variable.
1. I 5 Prt for P
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
4. V 5 ,wh for w
2.
A 5 :r2 for r
3. F 1 V 5 E 1 2 for V
5.
1
V 5 }3 :r2h for h
1
6. A 5 } (b1 1 b2)h for b1
2
BENCHMARK 2
C. Equations in Two Variables
EXAMPLE
Literal equation An equation, such as a formula, with two or more variables where the
coefficients and constants have been replaced by letters.
2. Use the Solution to a Literal Equation
EXAMPLE
After solving a
literal equation,
you can use unit
analysis to check
your work.
PRACTICE
Use the solution to the literal equation from the example
in Part 1 to solve 14 m + 6 4.
Solution:
y2b
}
x 5m
14 2 (24)
}5m
6
35m
Solution of literal equation.
Substitute 14 for y, 6 for x, and 4 for b.
Simplify.
Solve the given formula for the unknown variable. Then use the solution to answer the question.
m
7. The density d of a substance is given by d 5 } , where m is the mass in grams (g)
V
and V is volume in cubic centimeters (cm3). A scientist completely fills a beaker
with 28 g of a substance that has density 0.4375 g/cm3. What is the beaker’s
volume?
1600
8. The strength s of a radio signal is given by s 5 }
, where d is the distance in
d2
miles from the transmitter. If s is 100, how far are you from the transmitter?
Algebra 1
Benchmark 2 Chapters 3 and 4
27
Name ———————————————————————
Date ————————————
BENCHMARK 2
(Chapters 3 and 4)
9. A roller coaster car goes down a hill and
then makes a loop. The velocity v of
}
the car at the top of the loop is v 5 8Ïh 2 2r , where h is the hill’s height and r
is the loop’s radius. If v is 32 ft/s and r is 15 ft, how tall is the hill?
3. Rewrite an Equation
Remember to
first isolate the
term containing
the dependent
variable. Then
multiply or divide
to isolate the
variable.
PRACTICE
Write 3x 5y 15 so that y is a function of x.
Solution:
3x 2 5y 5 15
Write original equation.
25y 5 15 2 3x
3
y 5 23 1 }5 x
Subtract 3x from each side.
Divide each side by 5.
Write the equation so that y is a function of x.
10. 2x 2 y 5 10
3
13. } y 2 2x 5 12
4
11.
8 1 3y 5 24x
12. 9y 1 27 5 2x
14.
2
5x 1 }5 y 5 30
15. 224 2 16y 5 8x
Quiz
Solve the literal equation for the specified variable.
1. P 5 4, for ,
2. V 5 :r2h for h
1
3. s 5 } (a 1 b 1 c) for a
2
4. S 5 :r, 1 :r2 for ,
5. h 5 216t2 1 vt 1 c for v
6. S 5 2,w 1 2wh 1 2,h for w
Solve the given formula for the unknown variable. Then use the solution
to answer the question.
}
P
7. For an electrical circuit, I 5 } gives the relationship between amperes of
R
Ï
current I, watts of power P, and ohms of resistance R. For a certain circuit, I is
5 amperes and P is 75 watts. What is the circuit’s resistance?
8. The sum s of the interior angles of an n-sided polygon is s 5 (n 2 2)180. If the
sum of the interior angles of a polygon is 2340, how many sides does it have?
}
c 2 Ïc
9. The formula e 5 }
gives the efficiency e of a car’s engine. The variable c
c
is the engine’s compression ratio. If an engine has e 5 0.75, what is the
compression ratio?
Write the equation so that y is a function of x.
28
10. 6y 2 3x 5 212
11.
3x 1 7y 5 14
12. 7 2 3y 5 21x
13. 24x 2 5y 5 9
14.
2 1 3y 5 28x
15. 24y 1 36 5 224x
Algebra 1
Benchmark 2 Chapters 3 and 4
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
BENCHMARK 2
C. Equations in Two Variables
EXAMPLE