Question

11．已知關(guān)于x，y的方程組$\left\{\begin{array}{l}{x+y=5}\\{4ax+5by=-22}\end{array}\right.$與$\left\{\begin{array}{l}{2x-y=1}\\{ax-by-8=0}\end{array}\right.$有相同的解，求a，b的值．

Answer 1

分析 聯(lián)立不含a與b的方程求出x與y的值，代入剩下的方程求出a與b的值即可．

解答 解：由題意可將x+y=5與2x-y=1組成方程組$\left\{\begin{array}{l}{x+y=5}\\{2x-y=1}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入4ax+5by=-22，得8a+15b=-22①，
把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入ax-by-8=0，得2a-3b-8=0②，
①與②組成方程組，得$\left\{\begin{array}{l}{8a+15b=-22}\\{2a-3b-8=0}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=1}\\{b=-2}\end{array}\right.$．

點評 此題考查了二元一次方程組的解，方程組的解即為能使方程組中兩方程都成立的未知數(shù)的值．