Question

16．甲、乙两人同时解方程组$\left\{\begin{array}{l}{ax+y=3．①}\\{2x-by=2．②}\end{array}\right.$，甲看错了b，求得的解为$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$，乙看错了a，求得的解为$\left\{\begin{array}{l}{x=-1}\\{y=3}\end{array}\right.$，求（a+5b）²⁰¹²．

Answer 1

分析 把$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$代入①中求出a的值，再把$\left\{\begin{array}{l}{x=-1}\\{y=3}\end{array}\right.$代入②中求出b的值即可，再代入代数式解答即可．

解答 解：∵甲看错了b，求得的解为$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$，
∴把$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$代入①得，a-1=3，解得a=4；
∵乙看错了a，求得的解为$\left\{\begin{array}{l}{x=-1}\\{y=3}\end{array}\right.$，
∴把$\left\{\begin{array}{l}{x=-1}\\{y=3}\end{array}\right.$代入②得，-2-3b=2，解得b=-$\frac{4}{3}$，
把a=4，b=-$\frac{4}{3}$代入（a+5b）²⁰¹²=$（-\frac{8}{3}）^{2012}$=$（\frac{8}{3}）^{2012}$．

点评 本题考查的是二元一次方程组的解，熟知解二元一次方程组的加减消元法和代入消元法是解答此题的关键．