# An algebra problem by Kenneth Gravamen

Algebra Level 4

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 $$(x,y)$$ does the equation $$|x|+2|y|=100$$ have?

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