Systems of equations with 4 variables

[muted phoenix]

Hello everyone! I would like to ask for help on how to proceed with this system of equations with 4 variables. I already found the value of Z but I can't figure out how to move forward anymore because I'm so inattentive. What would be the next step? Btw the solution of this system is S={(-1,1,1,3)}
I would also like to apologize for the mess

[sweet fossil]

Hi there i can help!

Out of curiosity, are you familiar with gaussian elimination?

[sweet fossil]

also i see you got z=-1 but your solution says that z should =1

is that a typo in your original message or an error in your z calculation

[muted phoenix]

Thank you for the help

I just realized I misspelled

It should be 1

I will fix it

But I haven't learned the gaussian elimination yet

[sweet fossil]

Okay, that’s fine

So essentially here, once you’re gotten your Z value, you can simply find another set of equations (or previous already found) that just relate z and one other variable to a constant

and input your found value for z once you get there

for example you found

$-2y+4z-w=-9,and,5-2y=w$

[wide zinc]

OK32

[sweet fossil]

do you see how these two equations can be related to find the value of y or w if you input your z solution?

[muted phoenix]

Between these two equations specifically?

[muted phoenix]

I replaced z with its value, 1, and did the same with w, but y is giving 4.5.

[sweet fossil]

Then there is some error in the calculations that arrived at those two equations

work through the process again and see what you can get to

[muted phoenix]

-2y + 4z + w = -9
-2y +4(1) + (5 -2y) = -9
-4y + 9 = -9
-4y = -18
Y =4,5

[muted phoenix]

I think that must be it too

[sweet fossil]

Once you find one variable, the rest will pop out naturally from previous equations

[muted phoenix]

I will just do it from the beginning again

[muted phoenix]

Thank you!

[sweet fossil]

Ofc, send your work here again if you’re still having trouble and i can try and find exactly where the problem is

[muted phoenix]

Okiee

I've been stuck in this system for 1 hour and 30 minutes because I committed myself to not using chat gpt

[muted phoenix]

This is what endless doom scrolling and Ai dependence does to our brains 💔

[sweet fossil]

Don’t be too hard on yourself plenty of people have trouble with systems

that’s why I don’t even bother to work them out that way anymore, I always do gaussian elimination it’s much more intuitive to me

[muted phoenix]

Just by looking I also think it's simpler, but the teacher didn't even taught us because she's demanding another method to solve it

[sweet fossil]

Sadly part of learning early math, teachers can be very stuck on making you do it a certain way

[muted phoenix]

Exactly

I will do it again tomorrow,because its getting late at night

[muted phoenix]

Thanks again for your help!

[sweet fossil]

Sounds great, glad i was able to help a bit