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This one will be a little less finished...

5x - 2y + z = -3

              7y - 3z = -4

                4y + 3z = 26

Notice that we have a nice little 2 x 2 system that will give us the yand z answers...  Then, we'll just stick those into the first equation and we'll have x!

5x - 2y + z = -3
              7y - 3z = -4 and 4y + 3z = 26

Working the 2 x 2, eliminate the z...  to get y...  Then, use the y to pop 
the 
z...

( 7y - 3z = -4 ) + ( 4y + 3z = 26 ) = ( 11y = 22 ) ... y = 27y - 3z = -4 ... 7 ( 2 ) - 3 ( z ) = -4 ... 14 - 3z = -4 ... -3z = -18 ... z = 6

Now, stick y = 2 and z = 6 into the first equation to pop x:

5x - 2y + z = -3 ... 5x - 2 ( 2 ) + 6 = -3 ... 5x + 2 = -3 ... 5x = -5 ... x = -1

So, the answer is   ( -1 , 2 , 6 ) .

YOUR TURN:

       5x - 3y + 9z = -47

2x + 7y = 13

  4x + 5y = -1

* Notice that the 2 x 2 is x and y this time.  
You'll pop 
z in the last step.