Question 989590

Hi, I have a problem that deals with linear equations with three variables:
SOLVE:
x+y=7
y+z=8
x+2z=2

and no, I cannot simply use matrices to solve this question. I tried eliminating 'z' from the second and third equation, but I got stuck because I can't eliminate 'z' from the first equation. Please help and thank you so much to whoever helps!
<pre> x + y = 7_____y = 7 - x ------- eq (i)
    y + z = 8 ------ eq (ii)
   x + 2z = 2 ------ eq (iii)
7 - x + z = 8 ------ Substituting 7 - x for y in eq (ii)
  - x + z = 1 ------ eq (iv)
       3z = 3 ------ Adding eqs (iv) and (iii)
        z = {{{3/3}}}, or {{{highlight_green(1)}}}
Complete this by substituting 1 for z in eq (ii) to determine the value of y, and finally, substitute the value of y into eq (i) to get the value of x