# Mod equation

Algebra Level 3

For all real numbers, $$|x|$$ is defined as the absolute value of $$x$$; for example $$|4.2| = 4.2$$ and $$|-7| = 7$$. Given that $$x$$ and $$y$$ are integer, how many different solutions does the equation $$|x| + 2|y| = 100$$ have?

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