Question 1198509

Solve the system of equations.
X-2y+z=-3
-x+4y=10
2x-y+6z=7

The correct answer is one of the following.  Which one?

A) no solution 
B) x=2, y=3, z=1
C) x=-1, y=4,z=2
D) x=3, y=2, z=-1
E) x=-2, y=3, z=-4
<pre><font color = blue><font size = 4><b>   x - 2y + z = - 3 ---- eq (i)
 - x + 4y     =  10 ---- eq (ii)
  2x - y + 6z =  7 ----- eq (iii)
       2y + z = 7 ------ Adding eqs (i) & (ii) ----- eq (iv)

 2x - 4y + 2z = - 6 ----- Multiplying eq (i) by 2 ---- eq (v)
      3y + 4z = 13 ------ Subtracting eq (v) from eq (iii) ---- eq (vi)
      8y + 4z = 28 ------ Multiplying eq (iv) by 4 ---- eq (vii)
           5y = 15 ------ Subtracting eq (vi) from eq (vii)
           {{{highlight_green(matrix(1,5, highlight(y), "=", 15/5, "=", highlight(3)))}}}</b>
At this point, it's quite clear that it's either CHOICE B) or E).
       2(3) + z = 7 ------ Substituting 3 for y in eq (iv)
              z = 7 - 6 = 1 
Now that we've found that y = 3, and z = 1, there's NO DOUBT that CHOICE B) is correct.

If you wish, you can still continue on to determine the value of x - although it's not necessary - by substituting
3 for y in eq (ii), and solving for x. This way however, you will be 100% certain that CHOICE B) is indeed correct.</font></font></b></pre>