Question

4．若方程组$\left\{\begin{array}{l}{3x+4y=2}\\{2x-y=5}\end{array}\right.$与$\left\{\begin{array}{l}{\frac{a}{3}x-by=4}\\{ax+\frac{1}{2}by=5}\end{array}\right.$有相同的解，则a=3，b=2．

Answer 1

分析 先解方程组$\left\{\begin{array}{l}{3x+4y=2}\\{2x-y=5}\end{array}\right.$得$\left\{\begin{array}{l}{x=2}\\{y=-1}\end{array}\right.$，再把x=2，y=-1代入$\left\{\begin{array}{l}{\frac{a}{3}x-by=4}\\{ax+\frac{1}{2}by=5}\end{array}\right.$得$\left\{\begin{array}{l}{\frac{2}{3}a+b=4}\\{2a-\frac{1}{2}b=5}\end{array}\right.$，然后解关于a、b的方程组即可．

解答 解：解方程组$\left\{\begin{array}{l}{3x+4y=2}\\{2x-y=5}\end{array}\right.$得$\left\{\begin{array}{l}{x=2}\\{y=-1}\end{array}\right.$，
把x=2，y=-1代入$\left\{\begin{array}{l}{\frac{a}{3}x-by=4}\\{ax+\frac{1}{2}by=5}\end{array}\right.$得$\left\{\begin{array}{l}{\frac{2}{3}a+b=4}\\{2a-\frac{1}{2}b=5}\end{array}\right.$，
解方程组$\left\{\begin{array}{l}{\frac{2}{3}a+b=4}\\{2a-\frac{1}{2}b=5}\end{array}\right.$得$\left\{\begin{array}{l}{a=3}\\{b=2}\end{array}\right.$．
故答案为=3，2．

点评 本题考查了二元一次方程组的解：二元一次方程组的两个方程的公共解，叫做二元一次方程组的解．