Question

20．已知方程組$\left\{\begin{array}{l}{5x+y=7}\\{ax+5y=3}\end{array}\right.$與方程組$\left\{\begin{array}{l}{x-2y=8}\\{5x+by=2}\end{array}\right.$有相同的解，求a，b的值．

Answer 1

分析 解方程組$\left\{\begin{array}{l}{5x+y=7}\\{x-2y=8}\end{array}\right.$求得x，y的值，然后把x，y的值代入ax+5y=3和5x+by=2即可得到一個關于a，b的方程組，解方程組即可求得a，b的值．

解答 解：因為方程組$\left\{\begin{array}{l}{5x+y=7}\\{ax+5y=3}\end{array}\right.$與方程組$\left\{\begin{array}{l}{x-2y=8}\\{5x+by=2}\end{array}\right.$有相同的解，
所以它們的解是方程組$\left\{\begin{array}{l}{5x+y=7}\\{x-2y=8}\end{array}\right.$的解，
解方程組$\left\{\begin{array}{l}{5x+y=7}\\{x-2y=8}\end{array}\right.$得$\left\{\begin{array}{l}{x=2}\\{y=-3}\end{array}\right.$，
將$\left\{\begin{array}{l}{x=2}\\{y=-3}\end{array}\right.$代入$\left\{\begin{array}{l}{ax+5y=3}\\{5x+by=2}\end{array}\right.$得$\left\{\begin{array}{l}{2a-15=3}\\{10-3b=2}\end{array}\right.$，解得$\left\{\begin{array}{l}{a=9}\\{b=\frac{8}{3}}\end{array}\right.$．

點評 本題考查了方程組的解的定義，正確根據(jù)定義轉(zhuǎn)化成解方程組的問題是關鍵．