Question

8．甲、乙两个学生解方程组$\left\{\begin{array}{l}{ax+by=16}\\{cx-by=32}\end{array}\right.$，甲正确地解出$\left\{\begin{array}{l}{x=6}\\{y=-\frac{1}{2}}\end{array}\right.$，乙因把c看错了，而得到的解是$\left\{\begin{array}{l}{x=7.6}\\{y=-1.7}\end{array}\right.$，那么原题中a，b，c应分别为多少？

Answer 1

分析 根据题意把$\left\{\begin{array}{l}{x=7.6}\\{y=-1.7}\end{array}\right.$代入ax+by=16，再把$\left\{\begin{array}{l}{x=6}\\{y=-\frac{1}{2}}\end{array}\right.$，代入原方程组即可得a，b，c的方程组，求解即可．

解答 解：根据题意，得$\left\{\begin{array}{l}{6a-\frac{1}{2}b=16}\\{6c+\frac{1}{2}b=32}\\{7.6a-1.7b=16}\end{array}\right.$，解得$\left\{\begin{array}{l}{a=3}\\{b=4}\\{c=5}\end{array}\right.$．

点评 此题主要考查了二元一次方程组解的定义．以及解二元一次方程组的基本方法．