What does it mean when it asks to write the solution set with y arbitrary ?

Question

texaschic101 · Answer

I did a system of equations and found them to be infinite solutions. Now it says write solution set with y arbitrary. What does that mean ?

texaschic101 · Answer

@amistre64 ....please help

texaschic101 · Answer

does it mean set y as the subject and x can be any number being there is infinite solutions ?

anonymous · Answer

y is arbitrary means you want y to be your independent variable.
That means you want an equation with 
x = some expression involving y.
example: x = 2y -3

texaschic101 · Answer

Oh....I had it backwards....set x =.....thank you

texaschic101 · Answer

4x - 5y = 3
-8x + 10y = -6
------------
infinite solutions

4x - 5y = 3
4x = 5y + 3
x = 5/4y + 3/4 <-- so this is arbitrary ??

texaschic101 · Answer

@thomaster .....is this right ?

texaschic101 · Answer

@TuringTest ...please check this

thomaster · Answer

No idea xD I'm bad at math

texaschic101 · Answer

lol.....you could have fooled me, math genius. I got confused on it too

texaschic101 · Answer

@PixieDust1 ...can you help

texaschic101 · Answer

@ash2326 ...can you take a peek at this and tell me if it is correct

ash2326 · Answer

yes, it's correct.

texaschic101 · Answer

would it have mattered if I used the other equation ?

texaschic101 · Answer

-8x + 10y = -6
-8x = 10y - 6
x = -10/8y + 6/8
oh...they are the same once reduced.....so I guess it does not matter

texaschic101 · Answer

thank you ash :)

ash2326 · Answer

Yeah :)