# 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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