$解:\left\{\begin{array}{l}x+y=420(1) \\30 \% x+40 \% y=160 \times 80 \%(2)\end{array}\right. \\\text { 整理得: }\left\{\begin{array}{l}x+y=420(3) \\3 x+4 y=1280(4)\end{array}\right.\\(3) \times 4-(4) 得: x=400 \\把 x=400 代入(3)得: 400+y=420 ,\therefore y=20 \\\therefore\left\{\begin{array}{l}x=400 \\y=20\end{array}\right.$ $解:\left\{\begin{array}{l}\frac{x}{2}+\frac{y}{3}=16(1) \\\frac{x}{3}-\frac{y}{4}=5(2)\end{array}\right.\\(1) \times 2 得: x+\frac{2}{3} y=32(3) ,(2) \times 3 得: x-\frac{3}{4} y=15(4) \\(3) - (4)得: \frac{2}{3} y+\frac{3}{4} y=17 ,解得: y=12 \\则 \frac{x}{2}+4=16 ,解得: x=24 \\ \therefore 方程组的解为 \left\{\begin{array}{c}x=24 \\ y=12\end{array}\right. \\$ $解:(1) 把 x=5, y=6 ; x= -3, y=-10 代入 y=a x+b 中, \\得 \left\{\begin{array}{l}5 a+b=6, \\ -3 a+b=-10 \text {, }\end{array}\right. 解得 \left\{\begin{array}{l}a=2, \\ b=-4\end{array}\right. \\(2)由 (1) 得 y=2 x-4 , 把 x=1 代入, 得 y=2-4=-2 \\$ $解:因为两个方程组有相同的解, \\所以 \left\{\begin{array}{l}4 x-y=5, \\ 3 x+y=9\end{array}\right. 的解是它们的公共解, 解得 \left\{\begin{array}{l}x=2, \\ y=3 .\end{array}\right. \\把这组解分别代入另两个方程, 组成方程组 \left\{\begin{array}{l}2 a+3 b=-1, \\ 6 a+12 b=18,\end{array}\right. 解得 \left\{\begin{array}{l}a=-11, \\ b=7\end{array}\right. \\$ $解:因为 x * y=a x+b y, 2 * 1=4,-1 * 3=-9 ,\\所以 \left\{\begin{array}{l}2 a+b=4, \\ -a+3 b=-9,\end{array}\right. 解得 \left\{\begin{array}{l}a=3, \\ b=-2\end{array}\right. \\(2)因为 a=3 , b=-2 , 所以 x * y=3 x-2 y . 所以 1 * 5=3 \times 1-2 \times 5=3-10=-7 \\(3) 由已知 \left\{\begin{array}{l}m * n=-1, \\ (2 m) *\left(\frac{n}{2}\right)=4,\end{array}\right. 可得 \left\{\begin{array}{l}3 m-2 n=-1, \\ 6 m-n=4,\end{array}\right. 解得 \left\{\begin{array}{l}m=1, \\ n=2\end{array}\right. \\$
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