Question

15．已知$\left\{\begin{array}{l}{ax+by=5}\\{bx+ay=2}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=4}\\{y=3}\end{array}\right.$，則a=2，b=-1．

Answer 1

分析 把x與y的值代入方程組求出a與b的值即可．

解答 解：把$\left\{\begin{array}{l}{x=4}\\{y=3}\end{array}\right.$代入方程組得：$\left\{\begin{array}{l}{4a+3b=5①}\\{3a+4b=2②}\end{array}\right.$，
①×4-②×3得：7a=14，即a=2，
把a=2代入①得：b=-1，
故答案為：2；-1

點評 此題考查了解二元一次方程組，利用了消元的思想，消元的方法有：代入消元法與加減消元法．