0x+0y+0z=1

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Solution for 0x+0y+0z=1 equation: 


Simplifying
0x + 0y + 0z = 1

Anything times zero is zero.
0x + 0y + 0z = 1

Anything times zero is zero.
0 + 0y + 0z = 1

Anything times zero is zero.
0 + 0 + 0z = 1

Combine like terms: 0 + 0 = 0
0 + 0 = 1
0 = 1

Solving
0 = 1

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

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