## Elementary Linear Algebra 7th Edition

Because the system will always have at least one solution $x=0, \quad y=0, \quad z=0$.
On the right side of each equation will be zero. At $x=0$ and $y=0$ this will be true for all of the equations because on the left all of the terms will be zero as well. So there is always one solution $x=0$ and $y=0$ that satisfies all of the equations and thus they are consistent. Graphically the lines in $xy$ plane represented by these equations will all pass through the origin and so the origin will be a common point of intersection.