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Precalculus Functions and Graphs

Mark Dugopolski

Chapter 8

Systems of Equations and Inequalities - all with Video Answers

Educators

Section 1

Systems of Linear Equations in Two Variables

00:23

Problem 1

Fill in the blank.
A collection of two or more equations is a(n)______of equations.

Joshua Eastwood
Joshua Eastwood
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00:19

Problem 2

Fill in the blank.
A system of equations that has at least one solution is______.

Joshua Eastwood
Joshua Eastwood
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00:20

Problem 3

Fill in the blank.
A system of equations with no solution is______.

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:22

Problem 4

Fill in the blank.
A system of equations with exactly one solution is______.

Joshua Eastwood
Joshua Eastwood
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00:25

Problem 5

Fill in the blank.
A system of equations with infinitely many solutions is______.

Joshua Eastwood
Joshua Eastwood
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00:21

Problem 6

Fill in the blank.
Two systems with the same solution set are______ systems.

Joshua Eastwood
Joshua Eastwood
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00:47

Problem 7

Determine whether the given point is in the solution set to the given system.
$$\begin{aligned}
&(1,3)\\
&x+y=4\\
&x-y=-2
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:52

Problem 8

Determine whether the given point is in the solution set to the given system.
$$\begin{aligned}
&(-1,2)\\
&x+y=1\\
&2 x-3 y=-8
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:00

Problem 9

Determine whether the given point is in the solution set to the given system.
$$\begin{aligned}
&(-1,5)\\
&2 x+y=3\\
&x-2 y=-9
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:08

Problem 10

Determine whether the given point is in the solution set to the given system.
$$\begin{aligned}
&(3,2)\\
&3 x-y=7\\
&2 x+4 y=16
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:36

Problem 11

Solve each system by inspecting the graphs of the equations.
$$\begin{aligned}
&2 x-3 y=-4\\
&y=-2 x+4
\end{aligned}$$
(GRAPHS CANNOT COPY)

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:30

Problem 12

Solve each system by inspecting the graphs of the equations.
$$\begin{aligned}
x+2 y &=-1 \\
2 x+3 y &=-3
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:42

Problem 13

Solve each system by inspecting the graphs of the equations.
$$\begin{aligned}
&3 x-4 y=0\\
&y=\frac{3}{4} x+2
\end{aligned}$$
(GRAPHS CANNOT COPY)

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:52

Problem 14

Solve each system by inspecting the graphs of the equations.
$$\begin{aligned}
&x-2 y=-3\\
&y=\frac{1}{2} x+\frac{3}{2}
\end{aligned}$$
(GRAPHS CANNOT COPY)

Joshua Eastwood
Joshua Eastwood
Numerade Educator
03:53

Problem 15

Solve each system by graphing.
$$\begin{aligned}
&x+y=5\\
&x-y=1
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
03:07

Problem 16

Solve each system by graphing.
$$\begin{aligned}
2 x+y &=-1 \\
y-x &=5
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:26

Problem 17

Solve each system by graphing.
$$\begin{aligned}
&y=x-2\\
&y=-x+4
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:53

Problem 18

Solve each system by graphing.
$$\begin{aligned}
&y=-3 x\\
&x-2 y=7
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:04

Problem 19

Solve each system by graphing.
$$\begin{aligned}
&3 y+2 x=6\\
&y=-\frac{2}{3} x-1
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:45

Problem 20

Solve each system by graphing.
$$\begin{aligned}
&2 x+4 y=12\\
&2 y=6-x
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:35

Problem 21

Solve each system by graphing.
$$\begin{aligned}
&y=\frac{1}{2} x-3\\
&2 x-4 y=12
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:33

Problem 22

Solve each system by graphing.
$$\begin{aligned}
&y=-2 x+6\\
&4 x+2 y=8
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:45

Problem 23

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&y=2 x+1\\
&3 x-4 y=1
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:52

Problem 24

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&5 x-6 y=23\\
&x=6-3 y
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:11

Problem 25

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{array}{r}
x+y=1 \\
2 x-3 y=8
\end{array}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:05

Problem 26

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{array}{r}
x+2 y=3 \\
2 x+y=5
\end{array}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:53

Problem 27

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&y-3 x=5\\
&3(x+1)=y-2
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:17

Problem 28

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&2 y=1-4 x\\
&2 x+y=0
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:31

Problem 29

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&2 y=6-3 x\\
&\frac{1}{2} x+\frac{1}{3} y=3
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:36

Problem 30

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&2 x=10-5 y\\
&\frac{1}{5} x+\frac{1}{2} y=1
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:56

Problem 31

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{array}{c}
x+y=200 \\
0.05 x+0.06 y=10.50
\end{array}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:06

Problem 32

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&2 x+y=300\\
&\frac{1}{2} x+\frac{1}{3} y=80
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:55

Problem 33

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&y=3 x+1\\
&y=3 x-7
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:42

Problem 34

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&2 x+y=9\\
&4 x+2 y=10
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:09

Problem 35

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$
\begin{array}{l}
\frac{1}{2} x-\frac{1}{3} y=12 \\
\frac{1}{4} x-\frac{1}{2} y=1
\end{array}
$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:29

Problem 36

Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
$$\begin{aligned}
&0.05 x+0.1 y=10\\
&0.06 x+0.2 y=16
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:55

Problem 37

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
&x+y=20\\
&x-y=6
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:06

Problem 38

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
&3 x-2 y=7\\
&-3 x+y=5
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:15

Problem 39

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
x-y &=5 \\
3 x+2 y &=10
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:25

Problem 40

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
x-4 y &=-3 \\
-3 x+5 y &=2
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:38

Problem 41

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
&x-y=7\\
&y-x=5
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:52

Problem 42

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{array}{r}
2 x-y=6 \\
-4 x+2 y=9
\end{array}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:26

Problem 43

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
&2 x+3 y=1\\
&3 x-5 y=-8
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:45

Problem 44

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
-2 x+5 y &=14 \\
7 x+6 y &=-2
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:37

Problem 45

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
0.05 x+0.1 y &=0.6 \\
x+2 y &=12
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:20

Problem 46

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
0.02 x-0.04 y &=0.08 \\
x-2 y &=4
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:10

Problem 47

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{array}{l}
\frac{x}{2}+\frac{y}{2}=5 \\
\frac{3 x}{2}-\frac{2 y}{3}=2
\end{array}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:27

Problem 48

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\frac{x}{4}+\frac{y}{3}=0$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:22

Problem 49

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
3 x-2.5 y &=-4.2 \\
0.12 x+0.09 y &=0.4932
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:29

Problem 50

Solve each system by addition. Determine whether each system is independent, dependent, or inconsistent.
$$\begin{aligned}
1.5 x-2 y &=8.5 \\
3 x+1.5 y &=6
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:30

Problem 51

Classify each system as independent, dependent, or inconsistent without doing any written work.
$$\begin{aligned}
&y=5 x-6\\
&y=-5 x-6
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:33

Problem 52

Classify each system as independent, dependent, or inconsistent without doing any written work.
$$\begin{aligned}
&y=5 x-6\\
&y=5 x+4
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:33

Problem 53

Classify each system as independent, dependent, or inconsistent without doing any written work.
$$\begin{aligned}
&5 x-y=6\\
&y=5 x-6
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:01

Problem 54

Classify each system as independent, dependent, or inconsistent without doing any written work.
$$\begin{aligned}
&5 x-y=6\\
&y=-5 x+6
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:55

Problem 55

Solve each system by graphing the equations on a graphing calculator and estimating the point of intersection.
$$\begin{aligned}
&y=0.5 x+3\\
&y=0.499 x+2
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:43

Problem 56

Solve each system by graphing the equations on a graphing calculator and estimating the point of intersection.
$$\begin{aligned}
&y=2 x-3\\
&y=1.9999 x-2
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:33

Problem 57

Solve each system by graphing the equations on a graphing calculator and estimating the point of intersection.
$$\begin{aligned}
&0.23 x+0.32 y=1.25\\
&0.47 x-1.26 y=3.58
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:44

Problem 58

Solve each system by graphing the equations on a graphing calculator and estimating the point of intersection.
$$\begin{aligned}
&342 x-78 y=474\\
&123 x+145 y=397
\end{aligned}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:01

Problem 59

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
Two-Income Family Althea has a higher income than Vaughn and their total income is $\$ 82,000 .$ If their salaries differ by $\$ 16,000,$ then what is the income of each?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:24

Problem 60

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
A total of 76 young Republicans attended a strategy meeting. The number of females exceeded the number of males by $2 .$ How many of each gender were at the meeting?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:20

Problem 61

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
Carmen made $\$ 25,000$ profit on the sale of her condominium. She lent part of the profit to Jim's Orange Grove at $10 \%$ interest and the remainder to Ricky's Used Cars at $8 \%$ interest. If she received $\$ 2200$ in interest after one year, then how much did she lend to each business?

Supratim Pal
Supratim Pal
Numerade Educator
02:07

Problem 62

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
In 2008 Gerhart lost twice as much in the futures market as he did in the stock market. If his losses totaled $\$ 18,630,$ then how much did he lose in each market?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:36

Problem 63

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
The Springfield Zoo has different admission prices for adults and children. When Mr. and Mrs. Weaver went with their five children, the bill was $\$ 33$. If Mrs. Wong and her three children got in for $\$ 18.50$, then what is the price of an adult's ticket and what is the price of a child's ticket?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
03:31

Problem 64

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
At the Book Exchange, all paperbacks sell for one price and all hardbacks sell for another price. Tanya got six paperbacks and three hardbacks for $\$ 8.25,$ while Gretta got four paperbacks and five hardbacks for $\$ 9.25 .$ What was Todd's bill for seven paperbacks and nine hardbacks?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:06

Problem 65

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
The Valley Health Club sold a dozen memberships in one week for a total of $\$ 6000 .$ If male memberships cost $\$ 500$ and female memberships cost $\$ 500$, then how many male memberships and how many female memberships were sold?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:13

Problem 66

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
Mr. Thomas and his three children paid a total of $\$ 65.75$ for admission to Water World. Mr. and Mrs. Li and their six children paid a total of $\$ 131.50 .$ What is the price of an adult's ticket and what is the price of a child's ticket?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:34

Problem 67

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
A farmer has some cows and ostriches. One day he observed that his animals, which are normal, have 84 eyes and 122 legs. How many animals of each type does he have?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:56

Problem 68

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
The farmer's wife collects snakes and iguanas. One day she observed that her reptiles, which are normal, have a total of 60 eyes and 68 feet. How many reptiles of each type does she have?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:22

Problem 69

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
A rancher has some normal cows and horses. One day he observed that his animals have a total of 96 legs and 24 tails. How many animals of each type does he have?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:25

Problem 70

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
The rancher's wife raises snakes and white mice. One day she observed that her animals have a total of
78 eyes and 38 tails. How many animals of each type does she have?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:50

Problem 71

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
On Monday the office staff paid a total of S7.77 including tax for 3 coffees and 7 muffins. On Tuesday the bill was $\$ 14.80$ including tax for 6 coffees and 14 muffins. If the sales tax rate is $7 \%,$ then what is the price of a coffee and what is the price of a muffin?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:08

Problem 72

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
In Sociology 410 there are 55 more males than there are females. Two-thirds of the males and two-thirds of the females are graduating seniors. If there are 30 more graduating senior males than graduating senior females, then how many males and how many females are in the class?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:33

Problem 73

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
The results of a survey of students at Central High School concerning political party preference are given in the accompanying table. If 230 students preferred the Democratic party and 260 students preferred the Republican party, then how many students are there at CHS?
(TABLE CANNOT COPY)

Joshua Eastwood
Joshua Eastwood
Numerade Educator
03:09

Problem 74

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
Nutritional information for Rice Krispies and Grape-nuts is given in the accompanying table. How many servings of each would it take to get exactly $23 \mathrm{g}$ of protein and 215 g of carbohydrates? Which Write an equation for protein and another for carbohydrates.
(TABLE CANNOT COPY)

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:38

Problem 75

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
Distribution of Coin Types Isabelle paid for her $\$ 1.75$ lunch with 87 coins. If all of the coins were nickels and pennies, then how many were there of each type?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
03:00

Problem 76

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
Theodore has a collection of 166 old coins consisting of quarters and dimes. If he figures that each coin is worth two and a half times its face value, then his collection is worth $\$ 61.75 .$ How many of each type of coin does he have?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:13

Problem 77

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
Bird Mobile A wood carver is making a bird mobile, as shown in the accompanying figure. The weights of the horizontal bars and strings are negligible. The mobile will balance if the product of the weight and distance on one side of the balance point is equal to the product of the weight and distance on the other side. For what values of $x$ and $y$ will the mobile be balanced? Writul Write an equation for each balancing point.
(TABLE CANNOT COPY)

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:56

Problem 78

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
The Executive Inn rents a double room for $\$ 20$ more per night than a single. One night the motel took in $\$ 3949$ by renting 15 doubles and 26 singles. What is the rental price for each type of room?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:48

Problem 79

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
A civil engineer has a choice of two plans for renting furniture for her new office. Under Plan A she pays $\$ 800$ plus $\$ 150$ per month, while under Plan B she pays $\$ 200$ plus $\$ 200$ per month. For each plan, write the cost as a function of the number of months. Which plan is cheaper in the long run? For what number of months do the two plans cost the same?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:29

Problem 80

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
The 2008 tax rate schedule for a single taxpayer is given in the accompanying table (Internal Revenue Service, www.irs.ustreas.gov). Suppose the federal tax were simplified to be $\$ 100$ plus $25 \%$ of taxable income. Use a system of equations to find the taxable income at which a single taxpayer would pay the same amount of tax under the simplified plan as under the 2008 schedule.

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:10

Problem 81

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
Doctors often prescribe the same drugs for children as they do for adults. If $a$ is the age of a child and $D$ is the adult dosage, then to find the child's dosage $d$ doctors can use the formula $d=0.08 a D$ (Fried's rule) or $d=D(a+1) / 24$ (Cowling's rule). For what age do the two formulas give the same child's dosage?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:29

Problem 82

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
One plan for federal income tax reform is to tax =an individual's income in excess of $\$ 15,000$ at a $17 \%$ rate. Another plan is to institute a national retail sales tax of $15 \% .$ If =an individual spends $75 \%$ of his or her income in retail stores where it is taxed at $15 \%$, then for what income would the =amount of tax be the same under either plan?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:25

Problem 83

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
A 60 -ft truck doing 40 mph is approaching a 40 -ft truck doing 50 mph on a two-lane road. How long (in seconds) does it take them to pass each other?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:14

Problem 84

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
A 40 -ft truck doing 50 mph and a 60 -ft truck doing 40 mph are traveling in the same direction in adjacent lanes on an interstate highway. How long (in seconds) does it take the faster truck to pass the slower truck?

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:21

Problem 85

A system of equations can be used to find the equation of a line that goes through two points. For example, if $y=a x+b$ goes through $(3,5),$ then a and b must satisfy $3 a+b=5 .$ For each given pair of points, find the equation of the line $y=a x+b$ that
goes through the points by solving a system of equations.
$$(-3,9),(2,-1)$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:04

Problem 86

A system of equations can be used to find the equation of a line that goes through two points. For example, if $y=a x+b$ goes through $(3,5),$ then a and b must satisfy $3 a+b=5 .$ For each given pair of points, find the equation of the line $y=a x+b$ that
goes through the points by solving a system of equations.
$$(1,-1),(3,7)$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:50

Problem 87

A system of equations can be used to find the equation of a line that goes through two points. For example, if $y=a x+b$ goes through $(3,5),$ then a and b must satisfy $3 a+b=5 .$ For each given pair of points, find the equation of the line $y=a x+b$ that goes through the points by solving a system of equations.
$$(-2,3),(4,-7)$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:30

Problem 88

A system of equations can be used to find the equation of a line that goes through two points. For example, if $y=a x+b$ goes through $(3,5),$ then a and b must satisfy $3 a+b=5 .$ For each given pair of points, find the equation of the line $y=a x+b$ that goes through the points by solving a system of equations.
$$(-3,-1),(4,9)$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:30

Problem 89

Explain how you can tell (without graphing) whether a system of linear equations has one solution, no solutions, or infinitely many solutions. Be sure to account for linear equations that are not functions.

Joshua Eastwood
Joshua Eastwood
Numerade Educator
03:03

Problem 90

Write a step-by-step procedure (or algorithm) based on the addition method that will solve any system of two equations of the form $A x+B y=C .$ Ask a classmate to solve a system using your procedure.
Write a step-by-step procedure (or algorithm) based on the addition method that will solve any system of two equations of the form $A x+B y=C .$ Ask a classmate to solve a system using your procedure.

Erika Bustos
Erika Bustos
Numerade Educator
00:54

Problem 91

A system of equations can be used to find the equation of a line that goes through two points. For example, if $y=a x+b$ goes through $(3,5),$ then a and b must satisfy $3 a+b=5 .$ For each given pair of points, find the equation of the line $y=a x+b$ that goes through the points by solving a system of equations.
Write an independent system of two linear equations for which $(2,-3)$ is the solution. Ask a classmate to solve your system.

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:00

Problem 92

Write a dependent system of two linear equations for which $\{(t, t+5) | t \text { is any real number }\}$ is the solution set. Ask a classmate to solve your system.

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:21

Problem 93

Let $f(x)=8^{x}$ and $g(x)=4^{2-x} .$ Find the following.
a. $f(2 / 3)$
b. $g(3)$
c. $(f \circ g)(2)$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:19

Problem 94

What is the equation of the horizontal asymptote to the graph of $f(x)=3 e^{x-4}+5 ?$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
01:07

Problem 95

$$\text { Solve } 8^{x-3}=4^{x+5}$$

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:48

Problem 96

Find the equation of the axis of symmetry for the graph of $g(x)=-3 x^{2}-5 x+9$.

Joshua Eastwood
Joshua Eastwood
Numerade Educator
02:46

Problem 97

$$\text { Solve } 15 x^{2}-28 x+12 \leq 0$$.

Joshua Eastwood
Joshua Eastwood
Numerade Educator
03:08

Problem 98

Find the remainder when $x^{8}-2 x+1$ is divided by $x-2$.

Joshua Eastwood
Joshua Eastwood
Numerade Educator