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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