Systems of equations help

This seems like it requires a lot of intuition because I'm always having trouble figuring the right answers and get different answers...

Like here:

$\displaystyle 3x-5y+5z = 1$

$\displaystyle -5x-2y+3z = 0$

$\displaystyle 7x-y+3z = 0$

My work:

$\displaystyle -5x-2y+3z = 0$

$\displaystyle -7x+y-3z = 0$

$\displaystyle -12x-y = 0$

$\displaystyle 7x +y+3z = 0$

$\displaystyle

-5x+3z = 0$

$\displaystyle 5x+2y-3z=0$

$\displaystyle 2y = 0$

Inconsistent. And this isn't how you do it and I don't know why what I'm doing is wrong.

if i understand you correctly

Quote:

Originally Posted by

**A Beautiful Mind** This seems like it requires a lot of intuition because I'm always having trouble figuring the right answers and get different answers...

Like here:

$\displaystyle 3x-5y+5z = 1$

$\displaystyle -5x-2y+3z = 0$

$\displaystyle 7x-y+3z = 0$

My work:

$\displaystyle -5x-2y+3z = 0$

$\displaystyle -7x+y-3z = 0$

$\displaystyle -12x-y = 0$

$\displaystyle 7x +y+3z = 0$

$\displaystyle

-5x+3z = 0$

$\displaystyle 5x+2y-3z=0$

$\displaystyle 2y = 0$

Inconsistent. And this isn't how you do it and I don't know why what I'm doing is wrong.

(Thinking) if i understand you correctly you are eventually trying to find what each variable equals and the way to do that with a system of equations is to find what each variable equals all with one variable in it such as finding what y equals in terms of x and what z equals in terms of x.

Then insert those equalities into one of the original questions and find what x truly equals.

then plug this number into your equalities for y and z and there you have it.

I hope this answers your question and truly helps (Rofl)