Chapter 5 Solving Systems Of Linear Equations - 5.5 Solving Equations By Graphing Worksheet Page 6
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6USING TOOLS
OPEN-ENDED
37.
In Exercises 31 and 32, use a graphing
Find values for m and b so that the
solution of the equation mx + b = − 2x − 1 is
calculator to solve the equation.
x = −3.
0.7x + 0.5 = −0.2x − 1.3
31.
HOW DO YOU SEE IT?
38.
The graph shows the total
2.1x + 0.6 = −1.4x + 6.9
32.
revenue and expenses of a company x years after it
opens for business.
MODELING WITH MATHEMATICS
33.
You need to hire
a catering company to serve meals to guests at a
Revenue and Expenses
wedding reception. Company A charges $500 plus
y
$20 per guest. Company B charges $800 plus
$16 per guest. For how many guests are the total costs
6
expenses
(See Example 3.)
the same at both companies?
4
revenue
MODELING WITH MATHEMATICS
34.
Your dog is
2
16 years old in dog years. Your cat is 28 years old in
cat years. For every human year, your dog ages by
0
0
2
4
6
8
10
x
7 dog years and your cat ages by 4 cat years. In how
Year
many human years will both pets be the same age in
their respective types of years?
a. Estimate the point of intersection of the graphs.
b. Interpret your answer in part (a).
MATHEMATICAL CONNECTIONS
39.
The value of the
perimeter of the triangle (in feet) is equal to the value
of the area of the triangle (in square feet). Use a graph
to fi nd x.
x ft
6 ft
MODELING WITH MATHEMATICS
35.
You and a friend
race across a fi eld to a fence and back. Your friend has
(x − 2) ft
a 50-meter head start. The equations shown represent
you and your friend’s distances d (in meters) from the
THOUGHT PROVOKING
40.
A car has an initial value
fence t seconds after the race begins. Find the time at
of $20,000 and decreases in value at a rate of
which you catch up to your friend.
$1500 per year. Describe a different car that will be
∣
∣
You: d =
−5t + 100
worth the same amount as this car in exactly 5 years.
∣
∣
Specify the initial value and the rate at which the
Your friend: d =
−3
1
t + 50
—
value decreases.
3
MAKING AN ARGUMENT
The graphs of y = −x + 4
36.
ABSTRACT REASONING
and y = 2x − 8 intersect at the point (4, 0). So,
41.
Use a graph to determine the
sign of the solution of the equation ax + b = cx + d
your friend says the solution of the equation
−x + 4 = 2x − 8 is (4, 0). Is your friend correct?
in each situation.
Explain.
a. 0 < b < d and a < c
b. d < b < 0 and a < c
Maintaining Mathematical Proficiency
Maintaining Mathematical Proficiency
Reviewing what you learned in previous grades and lessons
(Section 2.1)
Graph the inequality.
x ≤ −2
n ≥ 9
c < −6
42.
43.
44.
45.
y > 5
Use the graphs of f and g to describe the transformation from the graph of f to the
graph of g.
(Section 3.6)
f(x) = x − 5; g(x) = f(x + 2)
f(x) = 6x; g(x) = −f(x)
46.
47.
f(x) = −2x + 1; g(x) = f(4x)
f(x) =
1
x − 2; g(x) = f(x − 1)
48.
49.
—
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266
Chapter 5
Solving Systems of Linear Equations
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