1. 用代入法解方程组$\begin{cases}y = 2x - 3,①\\3x - 2y = 8②\end{cases}$时,将方程①代入②中,所得的方程正确的是( )
A.$3x + 4x - 6 = 8$
B.$3x - 4x + 6 = 8$
C.$3x + 2x - 3 = 8$
D.$3x - 2x - 6 = 8$
A.$3x + 4x - 6 = 8$
B.$3x - 4x + 6 = 8$
C.$3x + 2x - 3 = 8$
D.$3x - 2x - 6 = 8$
答案:1. B
解析:
将①代入②,得$3x - 2(2x - 3) = 8$,去括号得$3x - 4x + 6 = 8$。
B
B
2. 用代入法解方程组$\begin{cases}3x + 4y = 2,①\\2x - y = 5②\end{cases}$时,比较合理的变形是( )
A.由①,得$x = \dfrac{2 - 4y}{3}$
B.由①,得$y = \dfrac{2 - 3x}{4}$
C.由②,得$x = \dfrac{5 + y}{2}$
D.由②,得$y = 2x - 5$
A.由①,得$x = \dfrac{2 - 4y}{3}$
B.由①,得$y = \dfrac{2 - 3x}{4}$
C.由②,得$x = \dfrac{5 + y}{2}$
D.由②,得$y = 2x - 5$
答案:2. D
解析:
用代入法解方程组时,应选择系数较简单的方程变形,方程②中$y$的系数为$-1$,变形较简便。
由②,得$y = 2x - 5$。
D
由②,得$y = 2x - 5$。
D
3. 用代入法解下列方程组:
(1)$\begin{cases}m = 3 - n,\\2m - 3n = 1;\end{cases}$
(2)$\begin{cases}2a + b = 3,\\b = 2a - 1;\end{cases}$
(3)$\begin{cases}x + y = 17,\\5x + 3y = 75;\end{cases}$
(4)$\begin{cases}2x + y = 1,\\3x - 2y = - 9;\end{cases}$
(5)$\begin{cases}2x + y = 7,\\2x + 4y = 16;\end{cases}$
(6)$\begin{cases}2x + 3y = 5,\\3x - y = 2;\end{cases}$
(7)$\begin{cases}3x + 8y = 5,\\4y = x + 5;\end{cases}$
(8)$\begin{cases}7x + 3y = 5,\\5x + 6y = - 8.\end{cases}$
(1)$\begin{cases}m = 3 - n,\\2m - 3n = 1;\end{cases}$
(2)$\begin{cases}2a + b = 3,\\b = 2a - 1;\end{cases}$
(3)$\begin{cases}x + y = 17,\\5x + 3y = 75;\end{cases}$
(4)$\begin{cases}2x + y = 1,\\3x - 2y = - 9;\end{cases}$
(5)$\begin{cases}2x + y = 7,\\2x + 4y = 16;\end{cases}$
(6)$\begin{cases}2x + 3y = 5,\\3x - y = 2;\end{cases}$
(7)$\begin{cases}3x + 8y = 5,\\4y = x + 5;\end{cases}$
(8)$\begin{cases}7x + 3y = 5,\\5x + 6y = - 8.\end{cases}$
答案:3. (1) $\begin{cases}m = 2,\ = 1\end{cases}$ (2) $\begin{cases}a = 1,\\b = 1\end{cases}$ (3) $\begin{cases}x = 12,\\y = 5\end{cases}$
(4) $\begin{cases}x = -1,\\y = 3\end{cases}$ (5) $\begin{cases}x = 2,\\y = 3\end{cases}$ (6) $\begin{cases}x = 1,\\y = 1\end{cases}$
(7) $\begin{cases}x = -1,\\y = 1\end{cases}$ (8) $\begin{cases}x = 2,\\y = -3\end{cases}$
(4) $\begin{cases}x = -1,\\y = 3\end{cases}$ (5) $\begin{cases}x = 2,\\y = 3\end{cases}$ (6) $\begin{cases}x = 1,\\y = 1\end{cases}$
(7) $\begin{cases}x = -1,\\y = 1\end{cases}$ (8) $\begin{cases}x = 2,\\y = -3\end{cases}$