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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