Caroline Wicker Presents...

Solving Systems of Equations

With Women Of History

 

Table of Contents:

Audrey Kathleen Hepburn-Ruston

Ferrer Dotti

(1929 - 1993)

Mother of two. Wife of Mel Ferrer and, after divorce, of Dr. Andrea Dotti. She was born in Brussels, Belgium and caught by German Nazi's while vacationing in Holland; she suffered from depression and malnutrition. After the war she took up ballet and modeling. She began her acting career soon after, but her big break was found playing in Roman Holiday which she won an Oscar for in 1953. Other classic movies she starred in include: Sabrina (1954), Funny Face (1957), Breakfast at Tiffany's (1961), My Fair Lady (1967). In 1988, after an early retirement, Audrey became an ambassador for the United Nations UNICEF until 1993. Through this program she had the opportunity to help children in Latin America and Africa. She died of colon cancer in 1993.

 

 

Jacqueline Lee Bouvier Kennedy Onnasis

(1929 - 1994)

Mother of two. Wife of John F. Kennedy Sr. who took presidential office as the 35th U.S. President in 1960, but was assassinated in Dallas, Texas in 1963. Jackie witnessed the murder along with the rest of America. She was an American icon even after she left the White House. Jackie went on to marry Aristotle Onasis in 1968 and work with Doubleday as an editor. She died from lymphoma in 1994 and was buried beside her first husband in Arlington Cemetary.

 

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Harriet Ross Tubman Davis

(1819 - 1913)

Harriet Tubman was born of purely African descent and into slavery. She was beaten from a very young age. She married a free African American, John Tubman. Fearing she would be relocated to a plantation in the south, Harriet escaped to Philadelphia with the help of a white friend. Once in Philadelphia she met William Still who was in association with the Underground Rail Road (a secret network of people that smuggled slaves to freedom and safety). He helped her get to Canada and later wrote a book about the UGRR and Harriet's role in it. Harriet helped approximately 300 people become "free," risking her own life each time. During the Civil War she served as a soldier, spy and nurse at Fortress Monroe, but was denied payment for these services. There she met Nelson Davis whom she later married and moved to Auburn, New York with. In 1908 she began a home for the sick and elderly. She died in 1913 and was buried at Fort Hill Cemetary with military honors.

 

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Substitution In A Word Problem

 
The drama club sold 1500 tickets for the end-of-year performance. Admission prices were $12 for adults and $6 for students.  The total amount collected at the box office was $16,200.  How many students attended the play?

1500 = # of tickets sold
$16,200 = total amount collected
$12 = cost of an adult ticket
$6  = cost of a student ticket

First evaluate the problem by reading it carefully and picking out the important parts.

$2x + $6y = $16,200
x + y = 1,500

Create equations expressing.  One will need to express the amount of money collected and the amount per ticket.  The second should express the number of tickets sold.

x + y = 1500
x = 1500 - y

Get x on a side by itself in equation 2.

12 (1500 – y) + 6y =16200

Plug in x into the first equation you created.

18000 – 12y + 6y = 16200
-6y  = -1800
y = 300 

Solve for y. 

Distribute, combine like terms, subtract, divide, and wah-la: you’ve found y (or how many adults attended the performance)!

x = 1500 – y
x = 1500 – (300)

Now substitute y into your modified equation 2.

x = 1200

Solve for x.

(1200, 300)
1200
students attended.
300 adults attended.

You now have your answer--1200.

 

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Agnes Gonxha Bojazhiu

(1910 - 1997)

At the age of 12, Gonxha, now known to many as Mother Teresa, felt a great calling from God. At age 18 she joined the Sisters Loreto, a missionary group doing work in India. In 1931, she took her official vow to become a nun and taught at St. Mary's High School in Calcutta until 1948, when she requested to work directly with the poor and dying. Her request was granted and also to start her own order, "The Missionaries of Charity," whose main mission is to love and care for those who no one can look after, in 1950. Mother Teresa continued to work with the people of India, while The Missionaries of Charity worked in over 40 different countries serving humbly those in wake of a natural disasters, shut-ins, refugees, alcoholics, homeless, and AIDS sufferers. She recieved the Nobel Peace Prize (1979), the Pope John XXIII Peace Prize (1971), Nehru Prize for promotion and understanding (1972), the Balzan Prize (1979), and the Templeton and Magsaysay awards. She died in 1997 from years of heart trouble and a bout of malaria.

 

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Annelies Marie Frank

(1929 - 1945)

Anne Frank was a German-Jewish teen who was forced to go into hiding during the Holocaust. She and her family, along with four others, spent 25 months during World War II in an annex of rooms above her father’s office in Amsterdam, the Netherlands. After being betrayed to the Nazis, Anne, her family, and the others living with them were arrested and deported to Nazi concentration camps. In March of 1945, nine months after she was arrested, she died of typhus at Bergen-Belsen. She was fifteen years old. Her diary, saved during the war by one of the family’s helpers, Miep Gies, was first published in 1947. Today, her diary has been translated into 67 languages and is one of the most widely read books in the world.

 

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Linear Combination
(with 3 variables)

 

3x + 2y + 4z = 11
2x -y+ 3z = 4
5x3y + 5z = -1

Solve for x, y, and z.

3x + 2y + 4z = 11
4x – 2y + 6z = 8

Multiply equation 2 by (2) in order to eliminate one of the variables—y.

7x + 10z = 19

Add equation 1 to equation 2. y is cancelled.

-6x + 3y – 9z = -12
5x – 3y + 5z = -1

Repeat these steps with equations 2 and 3 by multiplying equation 2 by (-3).  Remember you must eliminate the same variable—y—that you eliminated previously.

-x – 4z = -13

Add equation 2 to equation 3. y is, again, cancelled.

7x + 10z = 19
-x – 4z = -13

Now form a new system using the two equations you just created from the original three.

7x + 10z = 19
-7x – 28z = -91

You must get rid a variable once again.  Who’s next to go? Let’s pick x!  So multiply equation 2 by (7).

-18z = -72
     z = 4

Add the two equations. The x’s cancel and the z can be simplified.

7x + 10 (4) = 19

Substitute this z into one of the equations that you created earlier so we can find the value of x.

7x +  40 = 19
7x  = -21
 x = -3

Solve for x.

3x + 2y + 4z = 11
3(-3) + 2y + 4(4)= 11

Congratulations! You only have one more variable to find. And you know who that is? y!!  So go all the way back to one of the original equations and plug in x and z.

-9 + 2y + 16 = 11
 7 + 2y         = 11
       2y         = 4
         y         = 2

Solve for y.

Solution:
(-3, 2, 4)

X= -3
Y= 2
Z= 4

Now you have officially solved a 3 variable linear equation! Sounds complicated at first, but it’s not too bad is it?

 

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Lady Diana Frances Spencer

(1961 - 1997)

Mother of two. Diana, Princess of Wales was born on 1 July 1961 in Norfolk. She married The Prince of Wales at St Paul's Cathedral in London in 1981. During her marriage the Princess undertook a wide range of royal duties. Family was very important to the her. She gave birth to two sons - Prince William and Prince Henry (called Harry). After her divorce from The Prince of Wales, The Princess continued to be regarded as a member of the Royal Family. Until the end of her life she was involved with charities working to help children, homeless people and AIDS sufferers, as well as with the campaign to ban land mines.

 

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Graphing To Solve Equations

Remember: y=mx+b
m = slope
b = y intercept

y = 2x – 5
y = 7x

Solve by finding the points (x, y)

m1= 2/1
m2 = 7/1
b1= -5
b2= 0

Identify the slope and y intercept of each line from the equation.

*You can use a calculator to graph by entering the equations into Y= and then pressing the GRAPH button. You can search through the graph or press 2nd, GRAPH to see the intersection on the table.*

Graph the lines.

m is the rise of the line over the run.  b is where the line intersects the y axis. Find b and then use slope to determine the line.

(-1, -7)

Find the point of intersection; there’s your solution.

 

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I certainly hope you have enjoyed learning how to solve equations, and that you have become more familiar with some of the great women of our history. For more information you can visit the following links:
For information on some of the women mentioned on this page and more, visit: For more math help, check out:

 

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