Đáp án đúng: A
Giải chi tiết:Theo đề bài ta có: \(\left\{ \begin{array}{l}x - y = - 9\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\\y - z = - 10\,\,\,\,\,\,\,\,\left( 2 \right)\\z + x = 11\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 3 \right)\end{array} \right.\)
Cộng hai vế của \(\left( 1 \right),\,\,\left( 2 \right),\,\,\left( 3 \right)\) ta có:
\(\begin{array}{l}\left( {x - y} \right) + \left( {y - z} \right) + \left( {z + x} \right) = \left( { - 9} \right) + \left( { - 10} \right) + 11\\\,x - y + y - z + z + x\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( { - 19} \right) + 11\\\,\left( {x + x} \right) - \left( {y - y} \right) - \left( {z - z} \right) = - 8\\\,2x - 0 - 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - 8\\\,2x \,\,\,\,\,\,\,\,\, = - 8\\\,x \,\,\,\,\,\,\,\,\, = - 4.\end{array}\)
Vì \(x - y = - 9 \Rightarrow y = x + 9 = - 4 + 9 = 5\).
Vì \(z + x = 11 \Rightarrow z = 11 - x = 11 - \left( { - 4} \right) = 11 + 4 = 15\)
Vậy \(x = - 4;\,\,y = 5;\,\,z = 15\).
Chọn A.
