x-z=-y

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Solution for x-z=-y equation: 


Simplifying
x + -1z = -1y

Solving
x + -1z = -1y

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add 'z' to each side of the equation.
x + -1z + z = -1y + z

Combine like terms: -1z + z = 0
x + 0 = -1y + z
x = -1y + z

Simplifying
x = -1y + z

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