How do I start this?
x + 3y - z = 2
x - 2y + 3z = 7
x + 2y - 5z = -21

Question

How do I start this?
x + 3y - z = 2
x - 2y + 3z = 7
x + 2y - 5z = -21

hartnn · Answer

subtract 1st from 2nd Equation, you will get one equation having y and z only--->(1)
subtract 3rd from  2nd Equation, you will get other equation having y and z only--->(2)
then u can solve (1)and(2) to get y and z

anonymous · Answer

I'm subtracting x from the second equation?

hartnn · Answer

u are subtracting equations,not x
like this: 
   x + 3y - z = 2
-  x - 2y + 3z = 7
___________________
  0  + 5y - 4z = -5
got this ?

anonymous · Answer

oh! and now I take that answer and subtract it from the third equation?

hartnn · Answer

ummmm, nopes, you subtract 3rd equation from 2nd equation similarly and again x gets eliminated

anonymous · Answer

ok I got 0 + 0 - 2z = 14

hartnn · Answer

y doesn't get cancelled......     
     x - 2y + 3z = 7
 -   x + 2y - 5z = -21
-------------------
     0  -4y +8z = 28

did u understand these 2 subtractions? these are term by term subtraction.

anonymous · Answer

so all the positive signs get turned to negative ones?

hartnn · Answer

yes,and all negative turns into positive
 (x - 2y + 3z = 7)  - ( x + 2y - 5z = -21)

anonymous · Answer

okay, now from here what do i do?

hartnn · Answer

u got 2 equations in y and z only!
can u solve it ?

anonymous · Answer

y +4z = 23?

hartnn · Answer

-4y +8z = 28
 5y - 4z = -5
can u solve these 2 ?

anonymous · Answer

do i substitute?

hartnn · Answer

there are several methods, which method are u comfortable with?
substitution , elimination ...

anonymous · Answer

i get lost once i get to 8z = 4y + 28

hartnn · Answer

divide by 2 on both sides, what u get ?

anonymous · Answer

where does the 2 come from?

anonymous · Answer

4z = 2y + 14 ?

hartnn · Answer

8z = 4y + 28
but there is -4z in other equation, right ?
so how would i make 4z from 8 z ?

anonymous · Answer

oh i see now. so now i have 4z = 2y + 14 and 5y - 4z = -5

hartnn · Answer

yes.
so put the expression of 4z u got in 5y - 4z = -5
and find y

anonymous · Answer

y = -1?

hartnn · Answer

5y-2y-14=-5
3y = 14-5
3y=9
y=?

anonymous · Answer

3

hartnn · Answer

did u get how ?

anonymous · Answer

yeah I think so, let me try to solve the rest of it

anonymous · Answer

is it x = -2,y = 3, z = 5?

hartnn · Answer

absolutely correct!
good work :)