Solve for real numbers x, y, and z Graph the 3 equations with
Graphing Calculator as 3D. The image shows three intersecting
tubes with elliptical cross-sections. Click here to open a GCF
file. (You must have Graphing Calculator 3.5 to open this file
but the image could be graphed with other software.) Opening in
GC 3.5 allows the image to rotate ans show different
perspectives. Examining the 3D image will not provide a solution
but it may suggest where to look. For example it appear the
three tubes may have a common point in the region where x, y,
and z are positive. Try fixing one of the variables -- for
example replace z with k -- and examine some 2D graphs for
different k. These are contour plots for each z = k plane. One
solution is very close to (x, y, x) = (1.71674, 3.05009, 5.679).