Question

12．已知方程组$\left\{\begin{array}{l}{ax-by=4}\\{ax+by=0}\end{array}\right.$的解为$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，则2a+3b的值为-4．

Answer 1

分析 把$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入方程组可得到关于a、b的二元一次方程组，可求得a、b的值，可求得答案．

解答 解：∵方程组$\left\{\begin{array}{l}{ax-by=4}\\{ax+by=0}\end{array}\right.$的解为$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，
∴$\left\{\begin{array}{l}{2a-b=4}\\{2a+b=0}\end{array}\right.$，解得$\left\{\begin{array}{l}{a=1}\\{b=-2}\end{array}\right.$，
∴2a+3b=2×1+3×（-2）=2-6=-4．
故答案为：-4．

点评 本题主要考查方程组的解的概念，掌握方程组的解满足方程组中的每一个方程是解题的关键．