1. Systems of Equations
Lesson 5.2.6
Nome, Alaska
1925
Balto

2. Prior In Chapter 5, we have been focusing on System of Equations.
So far, you have learned 3 different methods for finding solutions.
1) You can graph the equations and the
point of intersection is the solution.
2) You can use the substitution method.
3) You can use the elimination method.

3. Today
Today… We will be working with all three methods. Although, you can solve any system of equations with any of the three methods and get the same answer, sometimes one method stands out as a better choice to use. This will be our focus for the day. Before… We move on, let’s take a look at how systems of equations are used in real life.

4. Let’s make a Real-World Connection
In Lesson , when you were first learning about system of equations, you solved a problem involving the Iditarod Trail Sled Dog Race held yearly in Nome, Alaska.

5. Let’s make a Real-World Connection
Since our real-world connection today pertains again to the city of Nome, Alaska… Why don’t we take a minute to talk about the historical event that made this little town so famous.

6. Nome, Alaska is known for its Iditarod Sled Dog Race
Finish line –
Nome, Alaska

7. Iditarod Sled Dog Race
The annual race is in honor of the 20 sled dog teams who in 1925 raced to deliver a life saving diphtheria vaccine to Nome, Alaska.

8. Iditarod Sled Dog Race
Sled dog racer Leonhard Seppala was part of the relay team that delivered diphtheria vaccine to Nome, Alaska in January 1925.
Seppala's team, led by his dog Togo, traveled hundreds of miles through some of the most treacherous parts of Alaska's wilderness.
So why did a dog named Balto get all the glory instead of Togo?
Togo
Togo

9. Story of Balto
On January 21, 1925, several children in Nome, Alaska were diagnosed with diphtheria.
Diphtheria is a bacteria that invades the nose, mouth, and throat and can make it hard to swallow and even cause a patient to suffocate. Without the vaccine, the highly contagious disease would quickly spread to all of the children in Nome.
Balto, a Siberian Husky sled dog, became a hero after completing the final leg of a journey to deliver the desperately needed serum from Anchorage to Nome, Alaska.

10. Story of Balto
The only serum in Alaska was found to be at a hospital in Anchorage, nearly 1,000 miles away.
A train would be able to transport the medicine from Anchorage to Nenana, Alaska.
After that, transportation methods were almost non-existent. Packed ice prevented delivery to Nome by ship and blizzard conditions prevented transport by air.
It was finally decided that the only way to get the medicine over the remaining distance was by using a relay of dog sled teams.

11. Story of Balto
More than 20 mushers and their dog sled teams eventually took part in a Pony Express type relay.
They battled against temperatures that rarely rose above -40° and winds that were sometimes strong enough to knock over both the dogs and the sleds.
On February 1, 1925, the package was handed off
for the last time to a musher named Gunnar Kassen.
Gunnar’s sled dog team, led by Balto, set off to
cover the final leg to Nome.
Balto

12. Blizzard
Soon after Balto’s team left, a blinding blizzard began, dropping temperatures to
-50° and producing wind gusts over 50 mph.
Gunnar found himself unable to navigate, but Balto knew the trail well, and following his instincts, led the team through the blinding blizzard.
Over the next 20 hours, Balto slowly led his sled dog team over the final 53 miles.
On February 2 at 5.30 AM, the team finally arrived in Nome, successfully delivering the vaccine.

13. Nome, Alaska system of equation...

14. Real-World Connect (Word Problem)
It is currently -3 degrees in New York City, and it is expected to rise 2 degrees every day.
It is 5 degrees in Nome, Alaska and it is expected to drop 2 degrees every day.
After how many days will the temperature be the same in both cities?
Write a system for the situation and solve.
Now, graph.
Both cites would be ____ ̊ after ____ days.
New York City t = 2d – 3 or y = 2x – 3
Nome, Alaska t = -2d + 5 or y = -2x + 5
Both cities will be at 1 degrees after 2 days.
The lines should intersect at (2, 1) on coordinate plane.

15. Graphing Method Substitution Method Elimination Method
So when is the best time to use each method?
Here are some general guidelines you can use...
Graphing Method
If one or both equations are in
y = mx + b format and you are provided a coordinate plane.
2x + y = 15
y = 3x
Substitution Method
If either the “x” or “y” is isolated on one side of the equal sign.
x – y = 4
2x + y = -4
Elimination Method
If both equations are in standard form.
Ax + By = C

16. 4x + 10y = -6 -2x – 10y = 2 1) 2) y = 2x 4x – y = -4 3y = 3x + 1
Graphing Method
If one or both equations are in y = mx + b format and you are provided a coordinate plane.
Substitution Method
If either the “x” or “y” is isolated on one side of the equal sign.
Elimination Method
If both equations are in standard form.
Ax + By = C
Which would be best?
4x + 10y = -6
-2x – 10y = 2 1) 2)
y = 2x
4x – y = -4
Elimination 2. Substitution
3. Substitution 4. Elimination
ELIMINATION or SUBSTITUTION
ELIMINATION or SUBSTITUTION
3y = 3x + 1
x = 5 – y 3)
6x – 5y = -18
2x + 10y = 27 4)
ELIMINATION or SUBSTITUTION
ELIMINATION or SUBSTITUTION

17. Best to use Graphing Method
Select the graph of the system of equations:
Although substitution is an option here,
since you are given the graphs, it is probably
easier to go ahead and put the first equation in
y = mx + b format and identify the graph
using the y-intercept (b) and rate of change (m).

18. Closure
What happened to Balto and Togo?

19. In honor of Balto… Balto, at the Cleveland Museum of Natural History
New York City, Central Park. Statue of Balto.
Yes, this is the real Balto. They stuffed him!

20. Togo
After the successful serum run, Balto became the most famous canine of the run.
However, many mushers today consider Togo to be the true hero of the run. Seppala's team led by Togo covered the longest and most hazardous leg of the run.
In the movie, Togo was
portrayed as the villain.
Togo, at the Iditarod Trail Museum
Yes, Togo was stuffed too!

21. Northern Lights
Just thought these were pretty.
Nome, Alaska

22. Nome, Alaska in 1925.

24. End of PowerPoint