Tìm các số $x,{\rm{ }}y,{\rm{ }}z$ biết: $x + y = 11,{\rm{ }}y + z = 10,{\rm{ }}z + x =  - 3$.

Ta có: $x + y = 11,{\rm{ }}y + z = 10,{\rm{ }}z + x =  - 3$ nên

\(\begin{array}{l}\left( {x + y} \right) + \left( {y + z} \right) + \left( {z + x} \right) = 11 + 10 + \left( { - 3} \right)\\ \Leftrightarrow x + y + y + z + z + x = 21 + \left( { - 3} \right)\\ \Leftrightarrow \left( {x + x} \right) + \left( {y + y} \right) + \left( {z + z} \right) = 18\\ \Leftrightarrow 2x + 2y + 2z = 18\\ \Leftrightarrow 2\left( {x + y + z} \right) = 18\\ \Leftrightarrow x + y + z = 9\end{array}\)

Vậy \(x + y + z = 9.\)
+) $z = (x + y + z) - (x + y) = 9 - 11 =  - 2$
+)$x = (x + y + z) - (y + z) = 9 - 10 =  - 1$
+) $y = (x + y + z) - (x + z) = 9 - \left( { - 3} \right) = 12$
Vậy \(x =  - 1;y = 12;z =  - 2.\)