Question

16．甲、乙兩人同時解方程組$\left\{\begin{array}{l}{ax+y=3．①}\\{2x-by=2．②}\end{array}\right.$，甲看錯了b，求得的解為$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$，乙看錯了a，求得的解為$\left\{\begin{array}{l}{x=-1}\\{y=3}\end{array}\right.$，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，再代入代數(shù)式解答即可．

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

點(diǎn)評 本題考查的是二元一次方程組的解，熟知解二元一次方程組的加減消元法和代入消元法是解答此題的關(guān)鍵．