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2. 解下列方程组.
(1)$\left\{\begin{array}{l} y + 2 = 1 - x,\\ 3x + 2y = -3;\end{array}\right. $
解：$\left\{\begin{array}{l} x=-1,\\ y=0;\end{array}\right. $
(2)$\left\{\begin{array}{l} m - \frac{n}{2} = 2,\\ 2m + 3n = 12.\end{array}\right. $
解：$\left\{\begin{array}{l} m=3,\\ n=2.\end{array}\right. $

答案：
(1) $\left\{\begin{array}{l} x=-1,\\ y=0;\end{array}\right. $
(2) $\left\{\begin{array}{l} m=3,\\ n=2.\end{array}\right. $

3. 已知方程组$\left\{\begin{array}{l} \frac {14}{5} x + \frac {12}{5} y = 8,\\ \frac {12}{5} x - \frac {14}{5} y = 2\end{array}\right. $中，$x$、$y$的系数部分已经模糊不清，但知道两个$□$表示同一个数，两个$\triangle$也表示同一个数，且$\left\{\begin{array}{l} x = 2,\\ y = 1\end{array}\right. $是这个方程组的解. 你能写出原方程组吗?

答案： 设 $□=a,△=b$, 则 $\left\{\begin{array}{l} ax+by=8,\\ bx-ay=2.\end{array}\right. $ 将 $\left\{\begin{array}{l} x=2,\\ y=1\end{array}\right. $ 代入方程组, 解得 $\left\{\begin{array}{l} a=\frac {14}{5},\\ b=\frac {12}{5}.\end{array}\right. $ 则原方程组为 $\left\{\begin{array}{l} \frac {14}{5}x+\frac {12}{5}y=8,\\ \frac {12}{5}x-\frac {14}{5}y=2.\end{array}\right. $

1. (四川眉山最新中考题)我国古代数学名著《九章算术》记载：“今有牛五、羊二，直金十九两；牛二、羊三，直金十二两. 问牛、羊各直金几何?”题目大意是：$5$头牛、$2$只羊共$19$两银子；$2$头牛、$3$只羊共$12$两银子，每头牛、每只羊各多少两银子? 设$1$头牛$x$两银子，$1$只羊$y$两银子，则可列方程组为(A)
A. $\left\{\begin{array}{l} 5x + 2y = 19,\\ 2x + 3y = 12\end{array}\right. $
B. $\left\{\begin{array}{l} 5x + 2y = 12,\\ 2x + 3y = 19\end{array}\right. $
C. $\left\{\begin{array}{l} 2x + 5y = 19,\\ 3x + 2y = 12\end{array}\right. $
D. $\left\{\begin{array}{l} 2x + 5y = 12,\\ 3x + 2y = 19\end{array}\right. $

答案： A

2. (浙江宁波最新中考题)我国古代数学名著《九章算术》中记载：“粟米之法：粟率五十；粝米三十. 今有米在十斗桶中，不知其数. 满中添粟而春之，得米七斗. 问故米几何?”意思为：$50$斗谷子能出$30$斗米，即出米率为$\frac{3}{5}$. 今有米在容量为$10$斗的桶中，但不知道数量是多少. 再向桶中加满谷子，再春成米，共得米$7$斗. 问原来有米多少斗? 如果设原来有米$x$斗，向桶中加谷子$y$斗，那么可列方程组为(A)
A. $\left\{\begin{array}{l} x + y = 10,\\ x + \frac{3}{5}y = 7\end{array}\right. $
B. $\left\{\begin{array}{l} x + y = 10,\\ \frac{3}{5}x + y = 7\end{array}\right. $
C. $\left\{\begin{array}{l} x + y = 7,\\ x + \frac{5}{3}y = 10\end{array}\right. $
D. $\left\{\begin{array}{l} x + y = 7,\\ \frac{5}{3}x + y = 10\end{array}\right. $

答案： A