Really quick, simple math help needed >_>

[ertyu]

I'm doing some math right now and I've come across a system of equations:

6x - 5y + z = 6
x + y = 5

Now I know that there are infinitely many solutions, but I'm just not sure how to express that. At the bottom of the page it says "If there are infinitely many solutions, type an expression involving z for each coordinate where z represents all real numbers.

maybe it's just that I'm brainfarting but... what the hell does that mean?

[BarthelloSylph]

All I know is that the word describing your problem is "underspecification". Sorry

[0ni0n]

I'm doing some math right now and I've come across a system of equations:

6x - 5y + z = 6
x + y = 5

Now I know that there are infinitely many solutions, but I'm just not sure how to express that. At the bottom of the page it says "If there are infinitely many solutions, type an expression involving z for each coordinate where z represents all real numbers.

maybe it's just that I'm brainfarting but... what the hell does that mean?

It means to solve x and y using z in their expression.

1) 6x - 5y =6 - z
2) x + y = 5 >> 5x+ 5y = 25

1) + 2)
6x-5y+5x+5y=6-z+25
11x=31-z
x=(31-z)/11

substituting x = (31-z)/11 in x+y =5
y = 5 - (31-z)/11 = (55-31+z)/11=(24+z)/11

x=(31-z)/11
y=(24+z)/11

[ertyu]

It means to solve x and y using z in their expression.

1) 6x - 5y =6 - z
2) x + y = 5 >> 5x+ 5y = 25

1) + 2)
6x-5y+5x+5y=6-z+25
11x=31-z
x=(31-z)/11

substituting x = (31-z)/11 in x+y =5
y = 5 - (31-z)/11 = (55-31+z)/11=(24+z)/11

x=(31-z)/11
y=(24+z)/11

Aha! Ok thanks, it was staring at me in the face. I just kept doing stuff and would get z = 6 -6x +5y and wouldn't know what to do from there. Thanks!

[Demosthenes11]

matrices make it look so much cooler though ;(

[Ramor]

not many people learn how to do systems of equations with matrices though, we learned for math team and it's definitely easier/faster, but yeah...most people hate/fear matrices D:

[Kaylia]

not many people learn how to do systems of equations with matrices though, we learned for math team and it's definitely easier/faster, but yeah...most people hate/fear matrices D:

I hate matrices. They do the job, but it's so easy to lost track of what you're doing when you use them. Just take the determinant for exemple...most people have no fucking clue what it represent, yet they use it nearly every time there is a matrice.

[Ramor]

Yeah, they're just not taught as well as they could be (if taught at all), like I said I only know them from Math Team, among other various odd tricks that a lot of people I've come across in my physics/engineering courses that people weren't taught.

Like most things with math, if you're fluent with whatever it is you're working with the applications reach quite a bit beyond what most people would expect.