Precalculus

Michael Sullivan

Chapter 11 Systems of Equations and Inequalities - all with Video Answers

Educators

Section 1

Systems of Linear Equations: Substitution and Elimination

00:59

Problem 1

Solve the equation: $3 x+4=8-x$.

Brandon Fox

Numerade Educator

02:05

Problem 2

(a) Graph the line: $3 x+4 y=12$
(b) What is the slope of a line parallel to this line?

Brandon Fox

Numerade Educator

00:17

Problem 3

If a system of equations has no solution, it is said to be ____.

Brandon Fox

Numerade Educator

00:32

Problem 4

If a system of equations has one solution, the system is ____ and the equations are _____.

Brandon Fox

Numerade Educator

00:10

Problem 5

If the solution to a system of two linear equations containing two unknowns is $x=3, y=-2,$ then the lines intersect at the point ____.

Brandon Fox

Numerade Educator

00:32

Problem 6

If the lines that make up a system of two linear equations are coincident, then the system is ____ and the equations are ____.

Brandon Fox

Numerade Educator

01:06

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{array}{l}
2 x-y=5 \\
5 x+2 y=8
\end{array}\right.\\
&x=2, y=-1 ;(2,-1)
\end{aligned}$$

Kelly Hughes

Numerade Educator

00:49

Problem 8

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{array}{rr}
3 x+2 y= & 2 \\
x-7 y= & -30
\end{array}\right.\\
&x=-2, y=4 ;(-2,4)
\end{aligned}$$

Brandon Fox

Numerade Educator

00:57

Problem 9

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{array}{l}
3 x-4 y=4 \\
\frac{1}{2} x-3 y=-\frac{1}{2}
\end{array}\right.\\
&x=2, y=\frac{1}{2} ;\left(2, \frac{1}{2}\right)
\end{aligned}$$

Brandon Fox

Numerade Educator

01:20

Problem 10

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{array}{rr}
2 x+\frac{1}{2} y & =0 \\
3 x-4 y & =-\frac{19}{2}
\end{array}\right.\\
&x=-\frac{1}{2}, y=2 ;\left(-\frac{1}{2}, 2\right)
\end{aligned}$$

Kelly Hughes

Numerade Educator

00:30

Problem 11

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{array}{l}
x-y=3 \\
\frac{1}{2} x+y=3
\end{array}\right.\\
&x=4, y=1 ;(4,1)
\end{aligned}$$

Brandon Fox

Numerade Educator

00:41

Problem 12

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{aligned}
x-y &=3 \\
-3 x+y &=1
\end{aligned}\right.\\
&x=-2, y=-5 ;(-2,-5)
\end{aligned}$$

Brandon Fox

Numerade Educator

01:23

Problem 13

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{aligned}
3 x+3 y+2 z=& 4 \\
x-y-z=& 0 \\
2 y-3 z=&-8
\end{aligned}\right.\\
&x=1, y=-1, z=2\\
&(1,-1,2)
\end{aligned}$$

Kelly Hughes

Numerade Educator

01:10

Problem 14

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{array}{r}
4 x \quad-\quad z=7 \\
8 x+5 y-z=0 \\
-x-y+5 z=6
\end{array}\right.\\
&x=2, y=-3, z=1\\
&(2,-3,1)
\end{aligned}$$

Brandon Fox

Numerade Educator

01:32

Problem 15

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{array}{rr}
3 x+3 y+2 z= & 4 \\
x-3 y+z= & 10 \\
5 x-2 y-3 z= & 8
\end{array}\right.\\
&x=2, y=-2, z=2 ;(2,-2,2)
\end{aligned}$$

Brandon Fox

Numerade Educator

01:15

Problem 16

Verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned}
&\left\{\begin{array}{rr}
4 x-5 z= & 6 \\
5 y-z= & -17 \\
-x-6 y+5 z= & 24
\end{array}\right.\\
&x=4, y=-3, z=2 ;(4,-3,2)
\end{aligned}$$

Brandon Fox

Numerade Educator

01:13

Problem 17

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
x+y=8 \\
x-y=4
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:42

Problem 18

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
x+2 y=-7 \\
x+y=-3
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:55

Problem 19

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
5 x-y=21 \\
2 x+3 y=-12
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:15

Problem 20

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
x+3 y &=5 \\
2 x-3 y &=-8
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

01:00

Problem 21

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
3 x &=24 \\
x+2 y &=0
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

01:21

Problem 22

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
4 x+5 y &=-3 \\
-2 y &=-8
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:28

Problem 23

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
3 x-6 y=2 \\
5 x+4 y=1
\end{array}\right.$$

Kelly Hughes

Numerade Educator

02:48

Problem 24

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
2 x+4 y=\frac{2}{3} \\
3 x-5 y=-10
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:45

Problem 25

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
2 x+y=1 \\
4 x+2 y=3
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:35

Problem 26

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
x-y &=5 \\
-3 x+3 y &=2
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:04

Problem 27

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{c}
2 x-y=0 \\
4 x+2 y=12
\end{array}\right.$$

Kelly Hughes

Numerade Educator

02:37

Problem 28

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{lr}
3 x+3 y= & -1 \\
4 x+y= & \frac{8}{3}
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:20

Problem 29

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{r}
x+2 y=4 \\
2 x+4 y=8
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:15

Problem 30

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
3 x-y=7 \\
9 x-3 y=21
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:55

Problem 31

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
2 x-3 y &=-1 \\
10 x+y &=11
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:08

Problem 32

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
3 x-2 y=0 \\
5 x+10 y=4
\end{array}\right.$$

Kelly Hughes

Numerade Educator

02:03

Problem 33

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
2 x+3 y &=6 \\
x-y &=\frac{1}{2}
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:24

Problem 34

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
\frac{1}{2} x+y &=-2 \\
x-2 y &=8
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

03:38

Problem 35

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
\frac{1}{2} x+\frac{1}{3} y=3 \\
\frac{1}{4} x-\frac{2}{3} y=-1
\end{array}\right.$$

Kelly Hughes

Numerade Educator

04:19

Problem 36

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
\frac{1}{3} x-\frac{3}{2} y=-5 \\
\frac{3}{4} x+\frac{1}{3} y=11
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:55

Problem 37

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
3 x-5 y &=3 \\
15 x+5 y &=21
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:10

Problem 38

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
2 x-y= & -1 \\
x+\frac{1}{2} y= & \frac{3}{2}
\end{array}\right.$$

Andrija Isakov

Numerade Educator

05:32

Problem 39

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
\frac{1}{x}+\frac{1}{y}=8 \\
\frac{3}{x}-\frac{5}{y}=0
\end{array}\right.$$

Andrija Isakov

Numerade Educator

03:24

Problem 40

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
\frac{4}{x}-\frac{3}{y}=0 \\
\frac{6}{x}+\frac{3}{2 y}=2
\end{array}\right.$$

Andrija Isakov

Numerade Educator

04:09

Problem 41

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
x-y &=6 \\
2 x &-3 z=16 \\
2 y+z &=4
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

04:27

Problem 42

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
2 x+y & =-4 \\
-2 y+4 z & =0 \\
3 x & -2 z=-11
\end{array}\right.$$

Kelly Hughes

Numerade Educator

09:25

Problem 43

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x-2 y+3 z= & 7 \\
2 x+y+z= & 4 \\
-3 x+2 y-2 z= & -10
\end{array}\right.$$

Kelly Hughes

Numerade Educator

04:56

Problem 44

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
2 x+y-3 z= & 0 \\
-2 x+2 y+z= & -7 \\
3 x-4 y-3 z= & 7
\end{array}\right.$$

Andrija Isakov

Numerade Educator

03:43

Problem 45

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
x-y-z &=1 \\
2 x+3 y+z &=2 \\
3 x+2 y &=0
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

03:30

Problem 46

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
2 x-3 y-z=0 \\
-x+2 y+z=5 \\
3 x-4 y-z=1
\end{array}\right.$$

Kelly Hughes

Numerade Educator

03:38

Problem 47

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x-y-z= & 1 \\
-x+2 y-3 z= & -4 \\
3 x-2 y-7 z= & 0
\end{array}\right.$$

Andrija Isakov

Numerade Educator

03:04

Problem 48

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
2 x-3 y-z &=0 \\
3 x+2 y+2 z &=2 \\
x+5 y+3 z &=2
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:40

Problem 49

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
2 x-2 y+3 z &=6 \\
4 x-3 y+2 z &=0 \\
-2 x+3 y-7 z &=1
\end{aligned}\right.$$

Andrija Isakov

Numerade Educator

04:28

Problem 50

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{lr}
3 x-2 y+2 z= & 6 \\
7 x-3 y+2 z= & -1 \\
2 x-3 y+4 z= & 0
\end{array}\right.$$

Kelly Hughes

Numerade Educator

04:48

Problem 51

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x+y-z= & 6 \\
3 x-2 y+z= & -5 \\
x+3 y-2 z= & 14
\end{array}\right.$$

Kelly Hughes

Numerade Educator

03:14

Problem 52

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x-y+z= & -4 \\
2 x-3 y+4 z= & -15 \\
5 x+y-2 z= & 12
\end{array}\right.$$

Andrija Isakov

Numerade Educator

04:22

Problem 53

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x+2 y-z= & -3 \\
2 x-4 y+z= & -7 \\
-2 x+2 y-3 z= & 4
\end{array}\right.$$

Andrija Isakov

Numerade Educator

05:26

Problem 54

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
x+4 y-3 z &=-8 \\
3 x-y+3 z &=12 \\
x+y+6 z &=1
\end{aligned}\right.$$

Andrija Isakov

Numerade Educator

01:13

Problem 55

The perimeter of a rectangular floor is 90 feet. Find the dimensions of the floor if the length is twice the width.

Brandon Fox

Numerade Educator

02:14

Problem 56

The length of fence required to enclose a rectangular field is 3000 meters What are the dimensions of the field if it is known that the difference between its length and width is 50 meters?

Brandon Fox

Numerade Educator

02:38

Problem 57

In 2005 there was a total of 55 commercial and noncommercial orbital launches worldwide. In addition, the number of noncommercial orbital launches was one more than twice the number of commercial orbital launches. Determine the number of commercial and noncommercial orbital launches in 2005 .

Kelly Hughes

Numerade Educator

04:25

Problem 58

A movie theater charges $\$ 9.00$ for adults and $\$ 7.00$ for senior citizens. On a day when 325 people paid an admission, the total receipts were $\$ 2495 .$ How many who paid were adults? How many were seniors?

Kelly Hughes

Numerade Educator

01:54

Problem 59

A store sells cashews for $\$ 5.00$ per pound and peanuts for $\$ 1.50$ per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $\$ 3,00$ per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

Brandon Fox

Numerade Educator

02:15

Problem 60

A recently retired couple needs $\$ 12,000$ per year to supplement their Social Security. They have $\$ 150,000$ to invest to obtain this income. They have decided on two investment options: AA bonds yielding $10 \%$ per annum and a Bank Certificate yielding $5 \%$.
(a) How much should be invested in each to realize exactly $\$ 12,000 ?$
(b) If, after 2 years, the couple requires $\$ 14,000$ per year in income, how should they reallocate their investment to achieve the new amount?

Brandon Fox

Numerade Educator

02:26

Problem 61

With a tail wind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the Piper.
(FIGURE CANNOT COPY)

Sheryl Ezze

Numerade Educator

01:39

Problem 62

The average airspeed of a single engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed?

Dharmendra Jain

Numerade Educator

04:36

Problem 63

$A$ restaurant manager wants to purchase 200 sets of dishes. One design costs $\$ 25$ per set, while another costs $\$ 45$ per set. If she only has $\$ 7400$ to spend, how many of each design should be ordered?

Kelly Hughes

Numerade Educator

02:57

Problem 64

One group of people purchased 10 hot dogs and 5 soft drinks at a cost of $\$ 35.00 .$ A second bought
7 hot dogs and 4 soft drinks at a cost of $\$ 25.25 .$ What is the cost of a single hot dog? A single soft drink?

Brandon Fox

Numerade Educator

03:35

Problem 65

The grocery store we use does not mark prices on its goods. My wife went to this store, bought three 1 -pound packages of bacon and two cartons of eggs, and paid a total of $\$ 13.45 .$ Not knowing that she went to the store, I also went to the same store, purchased two 1 -pound packages of bacon and three cartons of eggs, and paid a total of $\$ 11.45 .$ Now we want to return two 1 -pound packages of bacon and two cartons of eggs. How much will be refunded?

Brandon Fox

Numerade Educator

02:01

Problem 66

Pamcla requires 3 hours to swim 15 miles downstream on the Illinois River. The return trip upstream takes 5 hours. Find Pamela's average speed in still water. How fast is the current? (Assume that Pamela's speed is the same in each direction.)

Dharmendra Jain

Numerade Educator

02:32

Problem 67

A doctor's prescription calls for a daily intake containing 40 milligrams (mg) of vitamin $\mathrm{C}$ and $30 \mathrm{mg}$ of vitamin D. Your pharmacy stocks two liquids that can be used: one contains $20 \%$ vitamin $\mathrm{C}$ and $30 \%$ vitamin $\mathrm{D}$, the other $40 \%$ vitamin $\mathrm{C}$ and $20 \%$ vitamin D. How many milligrams of each compound should be mixed to fill the prescription?

Dharmendra Jain

Numerade Educator

01:49

Problem 68

A doctor's prescription calls for the creation of pills that contain 12 units of vitamin $B_{12}$ and 12 units of vitamin E. Your pharmacy stocks two powders that can be used to make these pills: one contains $20 \%$ vitamin $B_{12}$ and $30 \%$ vitamin $\mathrm{E}$, the other $40 \%$ vitamin $\mathrm{B}_{12}$ and $20 \%$ vitamin
E. How many units of each powder should be mixed in each pill?

Dharmendra Jain

Numerade Educator

06:10

Problem 69

Find real numbers $a, b,$ and $c$ so that the graph of the function $y=a x^{2}+b x+c$ contains the points $(-1,4),(2,3),$ and $(0,1)$.

Kelly Hughes

Numerade Educator

07:19

Problem 70

Find real numbers $a, b,$ and $c$ so that the graph of the function $y=a x^{2}+b x+c$ contains the points $(-1,-2),(1,-4),$ and $(2,4)$.

Kelly Hughes

Numerade Educator

02:48

Problem 71

In economics, the IS curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for goods in the economy. The LM curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for money in the economy. In an economy, suppose that the equilibrium level of income (in millions of dollars) and interest rates satisfy the system of equations
$$
\left\{\begin{array}{l}
0.06 Y-5000 r=240 \\
0.06 Y+6000 r=900
\end{array}\right.
$$
Find the equilibrium level of income and interest rates.

Kelly Hughes

Numerade Educator

02:34

Problem 72

In economics, the IS curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for goods in the economy. The IM curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for money in the economy. In an economy, suppose that the quilibrium level of income (in millions of dollars) and interest rates satisfy the system of equations
$$
\left\{\begin{array}{l}
0.05 Y-1000 r=10 \\
0.05 Y+800 r=100
\end{array}\right.
$$
Find the equilibrium level of income and interest rates.

Kelly Hughes

Numerade Educator

07:16

Problem 73

An application of Kirchhoff's Rules to the circuit shown on page 711 results in the following system of equations:
$$
\left\{\begin{aligned}
I_{2} &=I_{1}+I_{3} \\
5-3 I_{1}-5 I_{2} &=0 \\
10-5 I_{2}-7 I_{3} &=0
\end{aligned}\right.
$$
Find the currents $I_{1}, I_{2},$ and $I_{3}$
(FIGURE CANNOT COPY)

Suman Saurav Thakur

Numerade Educator

02:18

Problem 74

Electricity: Kirchhoff's Rules $\quad$ An application of Kirchhoffs Rules to the circuit shown results in the following system of equations:
$$
\left\{\begin{aligned}
I_{3} &=I_{1}+I_{2} \\
8 &=4 I_{3}+6 I_{2} \\
8 I_{1} &=4+6 I_{2}
\end{aligned}\right.
$$
Find the currents $I_{1}, I_{2},$ and $I_{3}$
(FIGURE CANNOT COPY)

Dharmendra Jain

Numerade Educator

06:41

Problem 75

A Broadway theater has 500 seats, divided into orchestra, main, and balcony seating. Orchestra scats sell for $\$ 50$, main scats for $\$ 35,$ and balcony scats for $\$ 25 .$ If all the seats are sold, the gross revenue to the theater is $\$ 17,100 .$ If all the main and balcony seats are sold, but only half the orchestra scats are sold, the gross revenue is $\$ 14,600 .$ How many are there of each kind of seat?

Andrija Isakov

Numerade Educator

04:55

Problem 76

A movie theater charges $\$ 8.00$ for adults, $\$ 4.50$ for children, and $\$ 6.00$ for senior citizens. One day the theater sold 405 tickets and collected $\$ 2320$ in receipts. Twice as many children's tickets were sold as adult tickets. How many adults, children, and senior citizens went to the theater that day?

Andrija Isakov

Numerade Educator

03:32

Problem 77

A dictitian wishes a patient to have a meal that has 66 grams ( $g$ ) of protein, $94.5 \mathrm{g}$ of carbohydrates, and 910 milligrams (mg) of calcium. The hospital food service tells the dietitian that the dinner for today is chicken, corn, and $2 \%$ milk. Each serving of chicken has $30 \mathrm{g}$ of protein, $35 \mathrm{g}$ of carbohydrates, and $200 \mathrm{mg}$ of calcium. Each serving of corn has 3 g of protein, 16 g of carbohydrates, and $10 \mathrm{mg}$. of calcium. Each glass of $2 \%$ milk has 9 g of protein, 13 g of carbohydrates, and 300 mg of calcium. How many servings of each food should the dictitian provide for the patient?

Dharmendra Jain

Numerade Educator

03:02

Problem 78

Kelly has $\$ 20,000$ to invest. As her financial planner, you recommend that she diversify into three investments: Treasury bills that yield $5 \%$ simple interest, Treasury bonds that yield $7 \%$ simple interest, and corporate bonds that yield $10 \%$ simple interest. Kelly wishes to earn $\$ 1390$ per year in income. Also, Kelly wants her investment in Treasury bills to be $\$ 3000$ more than her investment in corporate bonds. How much money should Kelly place in each investment?

Dharmendra Jain

Numerade Educator

04:59

Problem 79

One group of customers bought 8 deluxe hamburgers, 6 orders of large fries, and 6 large colas for $\$ 26.10 .$ A second group ordered 10 deluxe hamburgers, 6 large fries, and 8 large colas and paid $\$ 31.60$. Is there sufficient information to determine the price of each food item? If not, construct a table showing the various possibilities. Assume that the hamburgers cost between $\$ 1.75$ and $\$ 2.25,$ the fries between $\$ 0.75$ and $\$ 1.00,$ and the colas between $\$ 0.60$ and $\$ 0.90$

Darssan Eswaramoorthi

River Bluff High School

07:10

Problem 80

Use the information given in Problem 79. Suppose that a third group purchased 3 deluxe hamburgers, 2 large fries, and 4 large colas for $\$ 10.95 .$ Now is there sufficient information to determine the price of each food item? If so, determine each price.

Darssan Eswaramoorthi

River Bluff High School

03:10

Problem 81

Three painters, Beth, Bill, and Edie, working together, can paint the exterior of a home in 10 hours (hr). Bill and Edie together have painted a similar house in 15 hr. One day, all three worked on this same kind of house for 4 hr, after which Edie left. Beth and Bill required 8 more hr to finish. Assuming no gain or loss in efficiency, how long should it take each person to complete such a job alone?
(FIGURE CANNOT COPY)

Dharmendra Jain

Numerade Educator

02:27

Problem 82

Make up a system of three linear equations containing three variables that has:
(a) No solution
(b) Exactly one solution
(c) Infinitely many solutions Give the three systems to a friend to solve and critique.

Dharmendra Jain

Numerade Educator

02:15

Problem 83

Write a brief paragraph outlining your strategy for solving a system of two linear equations containing two variables.

Dharmendra Jain

Numerade Educator

02:09

Problem 84

Do you prefer the method of substitution or the method of elimination for solving a system of two linear equations containing two variables? Give reasons.

Brandon Fox

Numerade Educator