[tex] |x + y + 2| + |x - y| = 0 \\ \geqslant 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \geqslant 0 \\ \\ \rightarrow |x + y + 2| = 0 \: si \: | x - y| = 0 \\ \\ |x - y| = 0 \\ x - y = 0 \\ x = y \\ \\ |x + y + 2| = 0 \\ x = y \\ |2x + 2| = 0 \\ 2x + 2 = 0 \\ 2x = - 2 \\ x = - \frac{2}{2} \\ x = - 1 \\ x = y = - 1[/tex]
[tex] |x| + |y| = | - 1| + | - 1| = 1 + 1 = 2[/tex]
