Absolute Confusion

Algebra Level 4

\[\left| x \right| \, +\, x\, +\, y\, -\, z\, =\, 19\\ x\, +\, \left| y \right| \, -\, y\, +\, z\, =\, -18\\ x\, -\, y\, +\, \left| z \right| \, -\, z\, =\, 19\]

Let \(x\), \(y\), and \(z\) be integers that satisfy the equations above. What is the value of \(xz-y\)?

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