Question 1129918

Can someone help explain as, I'm confused to what the question is expecting the answer to be. 

Solve the following system of linear equations using elimination. (If there are infinitely many solutions, express x, y and z in terms of the parameter n. If there is no solution, enter NO SOLUTION.)

x + y − 5z = 6
x − 2z= 	2
2x −y − z= 0

My answer was z= - (-y+4)/ (3). x= 2- (-y+4)/ (3). 
<pre>Your answer is WRONG (I can't really decipher it, but then again, it doesn't have values for each variable), and other person's answer is just one of the INFINITELY MANY SOLUTIONS. This is why:
   x + y - 5z = 6 ------ eq (i)
   x     - 2z = 2 ------ eq (ii)
  2x - y - z = 0 ------- eq (iii)
  3x - 6z = 6 ---------- Adding eqs (i) & (iii) ------- eq (iv)
- 3x + 6z = - 6 -------- Multiplying eq (ii) by - 3 ----- eq (v)
        0 = 0 ---------- Adding eqs (iv) & (v)
The above is TRUE and so, this system has INFINITELY MANY solutions.