<PRE><B>Question 114169</B>
x+ y -4z=6
2x-5y+3z=2
x-6y+7z=-4
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Using the TI-83 Matrix function I find
the determinant of the coefficient matrix
is zero.  So there is no solution for this
system of equations.
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You can see why this happens if you add 
equation #1 to equation #3.  You get
2x-5y+3 = 2.  Therefore the system of 
equation is dependent; the three planes
are really just one plane.  
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Cheers,
Stan H.</PRE>