例1 下列方程组中,不是三元一次方程组的是 ( )
A. $\begin{cases}x + y = 3,\\y + z = 5,\\x + z = 4.\end{cases}$
B. $\begin{cases}x + y + z = 2,\\x - y + z = 0,\\x - z = 4.\end{cases}$
C. $\begin{cases}x = 5,\\x + y = 7,\\x + y + z = 6.\end{cases}$
D. $\begin{cases}x + y + 3z = 5,\\x - 3y = 4z,\\xy + yz = 1.\end{cases}$
A. $\begin{cases}x + y = 3,\\y + z = 5,\\x + z = 4.\end{cases}$
B. $\begin{cases}x + y + z = 2,\\x - y + z = 0,\\x - z = 4.\end{cases}$
C. $\begin{cases}x = 5,\\x + y = 7,\\x + y + z = 6.\end{cases}$
D. $\begin{cases}x + y + 3z = 5,\\x - 3y = 4z,\\xy + yz = 1.\end{cases}$
答案
例2 解下列三元一次方程组:
(1)$\begin{cases}x + y = 8,\\y + z = -2,\\z + x = -4;\end{cases}$ (2)$\begin{cases}3x - 2y + z = 5,\\2x + y - z = 6,\\4x + 3y + 2z = -1.\end{cases}$
(1)$\begin{cases}x + y = 8,\\y + z = -2,\\z + x = -4;\end{cases}$ (2)$\begin{cases}3x - 2y + z = 5,\\2x + y - z = 6,\\4x + 3y + 2z = -1.\end{cases}$
答案
1. 下列四组数值中,是方程组$\begin{cases}a + b + c = 0,\\2a - 3b + c = -9,\\3a + 2b - c = 2\end{cases}$的解的是 ( )
A. $\begin{cases}a = 0,\\b = 1,\\c = -1.\end{cases}$
B. $\begin{cases}a = -1,\\b = 2,\\c = -1.\end{cases}$
C. $\begin{cases}a = -1,\\b = 1,\\c = -2.\end{cases}$
D. $\begin{cases}a = 1,\\b = -2,\\c = 3.\end{cases}$
A. $\begin{cases}a = 0,\\b = 1,\\c = -1.\end{cases}$
B. $\begin{cases}a = -1,\\b = 2,\\c = -1.\end{cases}$
C. $\begin{cases}a = -1,\\b = 1,\\c = -2.\end{cases}$
D. $\begin{cases}a = 1,\\b = -2,\\c = 3.\end{cases}$
答案
2. 解三元一次方程组$\begin{cases}3x - y + z = 4 ①,\\2x - y - z = 12 ②,\\x + y + 2z = 6 ③,\end{cases}$若先消去$y$,组成关于$x$,$z$的方程组,则对方程组进行的变形是 ( )
A. ①+②,②+③
B. ①×2+③,②×2+③
C. ①+②,②×2+③
D. ①+③,②+③
A. ①+②,②+③
B. ①×2+③,②×2+③
C. ①+②,②×2+③
D. ①+③,②+③
答案
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