Question 1150775
.
<pre>

    x  - 2y + 2z = 3         (1)

    -x + 6y + 6z = 1         (2)

    2x - 7y - 2z = k         (3)



Add equations (1) and (2).  You will get

         4y + 8z = 4,    or, equivalently,

          y + 2z = 1.        (4)


Multiply equation (2) by 2  and then add to equation (3).  You will get

         5y + 10z = 2 + k,    or, equivalently,

          y +  2z = {{{(2+k)/5}}}.    (5)


Now compare equations (4) and (5).   They are compatible if and only if


    {{{(2+k)/5}}} = 1,  which is equivalent to

     2 + k = 5,

     k = 5 - 2 = 3.     <U>ANSWER</U>
</pre>

Solved.