SOLUTION: 7x+3y+6z=-7 -7x+8y+kz=-4, 7x+25y+28z=-30, for the system to be consistent we must have k≠?

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Question 987450: 7x+3y+6z=-7
-7x+8y+kz=-4,
7x+25y+28z=-30,
for the system to be consistent we must have k≠?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
 7x +  3y +  6z =  -7
-7x +  8y +  kz =  -4
 7x + 25y + 28z = -30

Add the 1st and 2nd equations:

 7x +  3y +     6z =  -7
-7x +  8y +     kz =  -4
------------------------
      11y + (6+k)z = -11        <--- equation A

Add the 2nd and 3rd equations:

-7x +  8y +      kz =  -4
 7x + 25y +     28z = -30
-------------------------
      33y + (k+28)z = -34       <--- equation B

Multiply equation A by -3 and add it to equation B

      -33y -       3(6+k)z =  33       <--- -3 times equation A
       33y +       (k+28)z = -34       <--- equation B
--------------------------------
          [-3(6+k)+(k+28]z =  -1
            [-18-3k+k+28]z =  -1
                  [10-2k]z =  -1

It will be consisitent if and only if the coefficient of z is not 0

                     10-2k ≠ 0
                       -2k ≠ -10
                         k ≠ 5                         
                
Edwin
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