1. 将三元一次方程组$\{\begin{array}{l} 5x + 4y + z = 0\ \ \textcircled{1},\\ 3x + y - 4z = 11\ \ \textcircled{2},\\ x + y + z = - 2\ \ \textcircled{3},\end{array} $经过步骤$\textcircled{1}-\textcircled{3}$和$\textcircled{3}×4+\textcircled{2}$消去未知数$z$后，得到的二元一次方程组是( )

A.$\{\begin{array}{l} 4x + 3y = 2,\\ 7x + 5y = 3\end{array} $
B.$\{\begin{array}{l} 4x + 3y = 2,\\ 23x + 17y = 11\end{array} $
C.$\{\begin{array}{l} 3x + 4y = 2,\\ 7x + 5y = 3\end{array} $

D.$\{\begin{array}{l} 3x + 4y = 2,\\ 23x + 17y = 11\end{array} $

A

$\textcircled{1}-\textcircled{3}$：$(5x + 4y + z)-(x + y + z)=0 - (-2)$，得$4x + 3y = 2$；
$\textcircled{3}×4+\textcircled{2}$：$4(x + y + z)+(3x + y - 4z)=4×(-2)+11$，即$4x + 4y + 4z + 3x + y - 4z=-8 + 11$，得$7x + 5y = 3$。
得到的二元一次方程组是$\{\begin{array}{l} 4x + 3y = 2\\ 7x + 5y = 3\end{array} $

2. 已知三元一次方程组$\{\begin{array}{l} 2x + y = 7,\\ 2y + z = 8,\\ 2z + x = 9,\end{array} $则$x + y + z$的值是( )

A.8
B.9
C.10
D.11

A

$\begin{cases}2x + y = 7, \quad (1) \\2y + z = 8, \quad (2) \\2z + x = 9. \quad (3)\end{cases}$
将方程$(1)$，$(2)$，$(3)$相加，得：
$2x + y+2y + z+2z + x = 7+8+9$，
$3x + 3y + 3z = 24$，
$3(x + y + z) = 24$，
$x + y + z = 8$。