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## 8th grade (Eureka Math/EngageNY)

### Course: 8th grade (Eureka Math/EngageNY) > Unit 4

Lesson 4: Topic D: Systems of linear equations and their solutions- Systems of equations: trolls, tolls (1 of 2)
- Systems of equations: trolls, tolls (2 of 2)
- Testing a solution to a system of equations
- Solutions of systems of equations
- Systems of equations with graphing
- Systems of equations with graphing
- Systems of equations with graphing: 5x+3y=7 & 3x-2y=8
- Systems of equations with graphing: y=7/5x-5 & y=3/5x-1
- Systems of equations with graphing: chores
- Systems of equations with graphing
- Systems of equations with elimination: 3t+4g=6 & -6t+g=6
- Systems of equations with elimination
- Systems of equations with elimination: x+2y=6 & 4x-2y=14
- Systems of equations with elimination: -3y+4x=11 & y+2x=13
- Systems of equations with elimination: 2x-y=14 & -6x+3y=-42
- Systems of equations with elimination: 4x-2y=5 & 2x-y=2.5
- Systems of equations with elimination: x-4y=-18 & -x+3y=11
- Systems of equations with elimination
- Systems of equations with elimination: 6x-6y=-24 & -5x-5y=-60
- Systems of equations with elimination challenge
- Systems of equations with substitution: 2y=x+7 & x=y-4
- Systems of equations with substitution
- Systems of equations with substitution: y=4x-17.5 & y+2x=6.5
- Systems of equations with substitution: -3x-4y=-2 & y=2x-5
- Systems of equations with substitution: 9x+3y=15 & y-x=5
- Systems of equations with substitution
- Systems of equations with substitution: y=-5x+8 & 10x+2y=-2
- Systems of equations with substitution: y=-1/4x+100 & y=-1/4x+120
- Systems of equations with elimination: apples and oranges
- Systems of equations with elimination: TV & DVD
- Systems of equations with elimination: King's cupcakes
- Systems of equations with elimination: Sum/difference of numbers
- Systems of equations with elimination: potato chips
- Systems of equations with elimination: coffee and croissants
- Systems of equations with substitution: coins
- Systems of equations with substitution: potato chips
- Systems of equations with substitution: shelves
- Systems of equations word problems
- Age word problem: Imran
- Age word problem: Ben & William
- Age word problem: Arman & Diya
- Age word problems
- Solutions to systems of equations: consistent vs. inconsistent
- Systems of equations number of solutions: fruit prices (1 of 2)
- Systems of equations number of solutions: fruit prices (2 of 2)
- Systems of equations number of solutions: y=3x+1 & 2y+4=6x
- Solutions to systems of equations: dependent vs. independent
- Number of solutions to a system of equations graphically
- Number of solutions to a system of equations graphically
- Forming systems of equations with different numbers of solutions
- Number of solutions to a system of equations algebraically
- Comparing Celsius and Fahrenheit temperature scales
- Converting Fahrenheit to Celsius

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# Converting Fahrenheit to Celsius

Converting Fahrenheit to Celsius. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- it is difficult the understand the formula of celsius and farenheit(14 votes)
- Just break the formula down in steps. Eg Farenheit to Celcius:

Take Temp in Celcius, 1. divide by 5 (easy math), 2. then multiply by 9, 3. then add 32.

So for 30 Celcius,

step 1. 30/5 = 6.

step 2. 6*9 = 54

step 3. 54 + 32 = 86 F

For the farenheit to Celcius, just reverse the order and do the opposite function in each steps:

1. _subtract 32

2. divide by 9

3. multiply by 5

Eg. So for 100 F =

step 1 (subtract 32) 100 - 32 = 68

step 2.(divide by 9) 68/9 = 7.56

step 3. (mult by 5) 7.56*5 = 37.8 C

Good rule of thumb is that Celcius is USUALLY a SMALLER number than Fahrenhet (until you are LESS than -40 F), that's a quick way to check to see if you did it right.(17 votes)

- How do you calculate Farenheit to Kelvin?(3 votes)
- You don’t. Convert to Celsius then to kelvin(1 vote)

- how is F and C equal at -40(3 votes)
- Since they are both scales measuring the same thing and are somewhat proportional, they are bound to meet or cross at some point.

If F = 9/5 C + 32,

then at C = - 40, then 9/5 (-40) + 32 = -72 + 32 = -40 F

Looking at the equation, we see that this point must meet 2 criteria

- be below 0 ˚C

Since the freezing point of water is higher than in the F scale than the C scale (32 ˚F vs. 0 ˚C) and both scales "grow" apart even further from there, the point of the scales crossing or intersecting would have to be below 0 ˚C, and below by more than 32˚ to bring the F scale down into negative territory as well

- a multiple of "5" on the C scale

So that the equation would give a whole number

For this particular equation, there is only 1 number that satisfies these conditions and fits the equation and that is -40.(4 votes)

- Why are there still several units for basic things like distance, weight and temperature?

Pros and cons?

The only positive thing about using different systems is that you can adjust the scale for a certain purpose, let's take kelvin for instance. Temperature is a measurement of atom's movement, so basing a temperature scale on that specific property seems like a handy thing when working with chemistry.

But in everyday life to me it seems like a better thing to share one standard system =)

Any thoughts?(4 votes)- I really agree with you on this. I feel like having a system that will make complete logical sense and be easy to remember/figure out would be so much better. Why is the US always the "wierd" one with things like this. I feel like the metric system and celsius would make things so much easier than having to do feet, and inches, and miles, and Farenheit.... just my opinion...(3 votes)

- in the2:15why is one? 10-9=9 not 1(3 votes)
- 9 and 10 are only one digit apart, so the answer is 1.(1 vote)

- why are temperatures greater for the fahrenheit scale than the celsius scale above 40 but lesser below 40?(2 votes)
- Is there a video on thermocouples? Because I can't seem to find any.(2 votes)
- Here is another great formula:

Fahrenheit to Celsius: F - 32 X 5 divided by 9

Celsius to Fahrenheit: C X by 9, then divide by 5, then add 32(2 votes) - I'm about to look super stupid, but I need help understanding Fahrenheit. I looked online and it states that Fahrenheit's freezing point is 39 degrees F. Then why is my fridge at 37 degrees F and nothing is frozen. Then my freezer is at 0 degrees F and everything is frozen. I don't understand. Why do we use Fahrenheit and not Celsius? HELP ME!(2 votes)
- one Fahrenheit equal to how much centigrade(2 votes)

## Video transcript

A thermometer in a science
lab displays the temperature in both Celsius and Fahrenheit. If the mercury in
the thermometer rises to 56 degrees
Fahrenheit-- they're giving us the
Fahrenheit temperature-- what is the corresponding
Celsius temperature? And then they give
us the two formulas, that if we know the
Celsius temperature, how do we figure out the
Fahrenheit temperature, or if we know the
Fahrenheit temperature, how do we figure out
the Celsius temperature. And these are actually
derived from each other, and you'll learn more about
that when you do algebra. And we also-- maybe
in another video-- will explain how
to derive these. It's actually kind
of interesting, involves a little
bit of algebra. But they gave us the formula. So they really just want us to
apply it, and maybe make sure we understand which
one we should apply. Well, they're giving us
the Fahrenheit temperature right here, so F is
going to be equal to 56. And they're asking us for
the Celsius temperature, so we need to figure out what
the Celsius temperature is. Well, in this one over here,
if you know the Fahrenheit temperature, then you can solve
for the Celsius temperature. So let's use this
right over here. So our Celsius
temperature is going to be 5/9 times the Fahrenheit
temperature-- the Fahrenheit temperature is 56 degrees
Fahrenheit-- minus 32. Well, 56 minus 32 is 24. So this is going to be
equal to 5/9 times 24. And this is the same thing
as 5 times 24, over 9. And before I even
multiply out 5 times 24, we can divide the numerator
and the denominator by 3. So let's do that. If we divide the numerator
by 3 and the denominator, we're not changing the value. 24 divided by 3 is 8. 9 divided by 3 is 3. So it becomes 5 times 8,
which is 40, over 3 degrees. And if we want to write
this as a number that makes a little bit more sense
in terms of temperature, let's divide 3 into 40 to get
the number of degrees we have. 3 goes into 4 one time. 1 times 3 is 3. Subtract. 4 minus 3 is 1. Bring down the 0. 3 goes into 10 three times. 3 times 3 is 9. Subtract. Get a 1. And then you could
bring down another 0. We now have a decimal
point over here. You're going to get a 0 here. 3 goes into, once
again, 10 three times. And this 3 is going
to repeat forever. So you could view this--
this is equal to 13.333-- it'll just keep repeating. This little line on top means
repeating-- degrees Celsius. Or you could say that, look,
3 goes into 40 13 times with a remainder of 1. So you could say that this is
also equal to 13, remainder 1. So 13 and 1/3 degrees Celsius. Either way, it works. But that's our
Celsius temperature when our Fahrenheit
temperature is 56 degrees.