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#1

Hi people. :slight_smile: My sister has a math problem she doesn’t know what to do with, and would be very grateful if someone could help her out a bit. :slight_smile:

Here are some examples of the problematic problems:
1 + 4 + D + 2E + F = 0
4 + 1 - 2D + E + F = 0
4 + 9 + 2D - 3E + F = 0

Her math book gives the answers as D = -1/2, E = 3/2, and F = -15/2. It says to review from algebra how to solve such systems of linear equations. But, she “only remembers working with two variables, and I don’t know where to start with three variables.”
So, how were these equations solved?

Thanks for your help, from both of us. :slight_smile:

#2

Muvlo Man, my algebra was about 35 years ago, but as I remember it, you transpose the variables, changing their signs, from one side of the equation to the other…This gives you a relationship of the remaining variables to the transposed ones, and you insert those relative values to solve the next part…

(I probably screwed up the explanation, but I hope it helps a little…It has been a LONG time!!! :rolleyes: )

#3

Hi Muvlo :slight_smile:
Here is a simple, step-by-step solution…

Original functions
1 + 4 + D + 2E + F = 0
4 + 1 - 2D + E + F = 0
4 + 9 + 2D - 3E + F = 0

Simplified functions
5 + D + 2E + F = 0
5 - 2D + E + F = 0
13 + 2D - 3E + F = 0

step 1: subtracting function 2 from function 1 in order to remove the F…
5 + D + 2E + F = 0
5 - 2D + E + F = 0
(5-5)+(D–2D)+(2E-E)+(F-F)=0
(0)+(3D)+(E)+(0)=0
:large_orange_diamond:3D+E=0

step 2: subtracting function 3 from function 2 in order to remove the F…
5 - 2D + E + F = 0
13 + 2D - 3E + F = 0
(5-13)+(-2D-2D)+(E–3E)+(F-F)=0
(-8)+(-4D)+(4E)+(0)=0
:large_orange_diamond:-8-4D+4E=0

step 3: using result of step 1 to get E…
3D+E=0
:large_orange_diamond:E=-3D

step 4: using result of step 3 in result of step 2 to get value of D…
-8-4D+4(-3D)=0
-8-4D-12D=0
-8-16D=0
8=-16D
:large_orange_diamond:D=-0.5

step 5: using result of step 4 in result of step 3 to get value of E…
E=-3D
E=-3*(-0.5)=1.5
:large_orange_diamond:E=1.5

step 6: using known values of D and E to evaluate F in the first original function…
5 + D + 2E + F = 0
5+(-0.5)+2(1.5)+F=0
5-.5+3+F=0
7.5+F=0
:large_orange_diamond:F=-7.5

step 7: Final result and verification…
:large_orange_diamond: D=-0.5, E=1.5, F=-7.5

verifying in last original function…
(This is an optional step intended to verify that we have not made any mistakes in the previous steps)
4 + 9 + 2D - 3E + F = 0
13+2(-0.5)-3(1.5)+(-7.5)=0
13-1-4.5-7.5=0
0=0 <=====true result

I hope this helps :slight_smile:
-Pixolator

#4

Pix you took me back a looooong way ! that brought back not so fond memories. I am glad you could help.
DeeVee

#5

OUTSTANDING lesson. Thank you very much, Pixolator! :+1: :sunglasses: :+1:

#6

Aaaahhh Pix…
I’m moving to the back of the room now! :rolleyes:
As DeeVee said, that took me back, too…Nice to see some people can still deal with these things! :wink:
(And thanks to you for the refresher, and Muvlo for taking me for a trip through Algebraic Memory Lane! :smiley: )

#7

Thanks Pix! She gets it now! And your explanation is so clear it made its way through the muddles of my own brain too! :smiley:

#8

Uhhh…yup…yeah…just like Pix says… :rolleyes:

#9

One things for sure, if the software thingy doesn’t fly, Pix could teach math class! :wink:

I’m impressed. What simple and clear explanations… :eek:

#10

this is how much i know math my teacher said what is (pie R Square) i raised my hand yelling? i know i know she said ok ÈZ what is it.
i said pie are not square there “round”
she told me to sit down because she wasn’t talking about apple “pie”