Im confused on this part where it says multiply to create opposites and dont know which equations to multiply to create those opposites please help.
#confused with linear systems in 3 variables and to find all 3 variables.
olive cape
vapid krakenBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
limber imp
The method is always the same
You need to combine equations to get rid of unknowns gradually
It is called Gauss elimination
If you are not familiar with such methods, you could use the last equation and write
$z = 4-2x-3y$
edgy turtleBOT
Daddy_314
limber imp
And replace z with this expression in the first two equations
You obtain a classic linear system with two unknowns
olive cape
whats a unknown
olive cape
oh
limber imp
The best way is the way that you can understand
olive cape
the way it showed me was like 2 pages long
it was long as hell
like to get the y value then the z value after the x value
limber imp
Yes
This method they are showing you (I assume)
Is called Gaussian elimination
In which the equations are combined
Until they form
A triangle
Like this:
..x + .. y + .. z = ...
...y + ... z = ....
... z = ...
In the end
olive cape
im so confused
limber imp
Im just telling you the general idea
Its normal to be confused
Since we have not solved anything yet
olive cape
ok
olive cape
um not really
limber imp
These systems happen in real life
olive cape
im trying to figure it out for the algebra 2 regents exam and im really bad at math
limber imp
Imagine you order drinks and food with 3 friends at a restaurant.
You go there with them but you forgot to look at the menu prices.
You go the first time:
You order 9 chicken soup, 3 rice and one diet coke
The waiter makes you pay 6$
The second time, you buy 8 chicken, 4 rice and 8 diet coke you pay 8$
The third time you go with your friends, buy two chicken, three rice and one diet coke and pay 4 dollars
So one day you call each other and try to figure out how much each item costs
You dont really know how much chicken, rice and diet coke cost
But you know the total you paid each time
So we can use the system of equations and try to guess the prices
Of each item on the menu
limber imp
Okay
Two apples and an orange cost 10$
One apple and one orange cost 6$
Can you guess (without any algebra) the price of each ?
olive cape
um
for the first one each apple could cost 2.5$ and the orange could be 5$
wait
each apple could cost 2 dollars and the orange could be 6 dollars
limber imp
for the first one each apple could cost 2.5$ and the orange could be 5$
This is true, it is a possibility if we only know the first information
olive cape
ok
limber imp
But if you confront this
With the second condition
It does not work
Because 2.5+5 = 7.5 which is not 6
limber imp
each apple could cost 2 dollars and the orange could be 6 dollars
And the same goes for this option
2+6 is 8 but we know that one apple and one orange cost 6
In fact, this is exactly the interesting part
We have two conditions
We need to satisfy
The possibilities you wrote only work for the first condition
limber imp
Two apples and an orange cost 10$
One apple and one orange cost 6$
Can you gues...
The apple and the orange are the same, for each equation
Its the same shop
With the same prices
For an orange and an apple
olive cape
ok
limber imp
So can you try again ?
limber imp
Let us check
If each apple costs 4 dollard and an orange 2
Then two apples + one orange costs 2 * 4 + 2 = 8+2=10
And indeed, 4+2=6
So this is correct !
Now this example is relatively simple
Because you could try some values
Mentally
And check them
The power of algebra is that we can apply mathematical rules to the equations and this solution will appear on its own
Without needing to guess anything
One way to do it is called substitution
Since $x+y = 6$ then we know for sure that $y = 6-x$
edgy turtleBOT
Daddy_314
limber imp
And since $2x+y = 10$ then we know for sure that
$2x+(6-x) = 10$
edgy turtleBOT
Daddy_314
limber imp
We replaced y by its value in terms of x by using the second condition
Into the first one
The word Substitution refers to "replacing"
olive cape
is that like the formula or something
olive cape
not really
limber imp
If I tell you $x+y = 6$
edgy turtleBOT
Daddy_314
limber imp
This is the same as saying that $y = 6-x$
edgy turtleBOT
Daddy_314
limber imp
Do you understand this ?
olive cape
um yeah i think so
limber imp
So saying x+y = 6 is the same as saying y = 6-x
olive cape
ok
edgy turtleBOT
Daddy_314
limber imp
We can replace it by $6-x$
edgy turtleBOT
Daddy_314
limber imp
So in the first equation, which is $2x+y = 10$
We spot a $y$ and we can replace it by $6-x$
edgy turtleBOT
Daddy_314
limber imp
So that the first equation becomes $2x+6-x = 10$
edgy turtleBOT
Daddy_314
limber imp
And this is great because now, we no longer have two unknown values x and y, we only have one unknown value
In this equation
It's like we untangled it
So if we manage to solve this equation and find x, we immediately can also find y
Solving this equation gives:
$2x+6-x = 10$
So
$2x-x = 10-6$
Therefore $x = 4$
edgy turtleBOT
Daddy_314
limber imp
This is the price of the apple
As you can see the power of algebra allowed us to find this without ever needing to take guesses
olive cape
ok
olive cape
why does 2x-x=10-6
limber imp
$2x+6-x = 10$
edgy turtleBOT
Daddy_314
limber imp
Do you agree that
$2x-x+6 = 10$
edgy turtleBOT
Daddy_314
olive cape
yes
limber imp
Adding 6 and subtracting x is the same as subtracting x and adding 6
And now, just like we did before
Saying $30+2 = 32$
Is the same as saying $30=32-2$
edgy turtleBOT
Daddy_314
limber imp
Saying $2x-x + 6 = 10$
Is the same as saying $2x-x = 10-6$
edgy turtleBOT
Daddy_314
olive cape
ok i get it better now
olive cape
ok
its really late for me rn its like 11pm
so i might go to sleep my eyes are like shutting rn
limber imp
Okay goodnight
Try to first learn systems of equations with only x and y
Before doing x,y and z
olive cape
ok
btw
this might be a dumb question
but im just wondering if i pass the regents with like a 65 but i failed 2 quarters with 57 do i still fail the class
limber imp
I dont know
How it works for you
If one thing weighs more than the other
You could use systems of equations to solve this
If you know the weights
Of exams
olive cape
oh
limber imp
limber imp
I think you need to
olive cape
i went before and it was one of the worst experiences ive ever had
limber imp
I dont think you need to go to a standard summer school
But
You do need to do some serious work
This summer
At your own pace
olive cape
my next class im taking for math is suppose to be statistics i think
limber imp
Preferably with some good support or institutions
You have a lot to learn
It seems
Or to remember
But you need to do it your ownbway
Own way
olive cape
most people in my class just remember what numbers to put where and kind of just memorize it
limber imp
And you also have a tendency to ask
"is this a formula"
Students who say this
Usually are about to
Memorize what I am saying
Which is a big nono
Its really important to develop critical thinking
And ask why we are doing this
And why this is like this
Etc.
olive cape
yeah thats what i wonder about a lot of the questions sometimes
olive cape
and a lot of times i get questions correct because i just memorize the order in what to do it in
do you know what i mean
limber imp
Yes I know
And this can only work
Up to a certain point
After which it wont
And also this creates a vicious cycle in which you forget things more and more
So your math level becomes fragile
The best skill to learn for you is to learn how to learn
Stop doing things mechanically
olive cape
its like 4 days until my regents and im just trying to study this green book thing hard
limber imp
Yea but
olive cape
so i dont think i have enough time to do that now
limber imp
There is life after this one exam
And whether you pass or fail it
A change is necessary
So do what you have to do for now
But
Theres a lot for you to work on
You have good critical thinking skills
But it seems zero confidence in your math skills
And a bit clueless
olive cape
how do i have good critical thinking skills 😭
limber imp
Change your ways and ull make progress
You do
Because when i asked about logic orange and apple, you found the values
And then afterwards
You know you had to ask for some algebra manipulation details
About y = 6-x
So in a way, you already know what you dont know
Which is a good starting point
Not all students have this
Now, the thing that is bad is that you say "ok" a lot and try to just "accept" whatever I say
"is this a formula or something"
This is the bad part
Never accept any detail that isnt crystal clear
It will take more time but u will become 10x more solid and confident
olive cape
ok thanks
im not too sure how to study rn though i guess i should just try to memorize this stuff in this book and then after ill try to understand what im doing
limber imp
olive cape
whats that suppose to mean 💀
olive cape
well im trying to pass the test rn
it took me like a hour to try and understand a simpler version of a problem im suppose to know for the test so im not sure what im suppose to do
limber imp
Ok but at least understand the basics of.algebraic manipulations
You cant even do a subtraction in equations
This is for sure on the test
Practice is necessary
olive cape
ok