Question

4．已知方程组$\left\{\begin{array}{l}{3x-y=5}\\{4x-7y=1}\end{array}\right.$的解也是方程组$\left\{\begin{array}{l}{ax-2y=4}\\{3x-by=5}\end{array}\right.$的解，则a=3，b=1，3a+2b=11．

Answer 1

分析 先解方程组$\left\{\begin{array}{l}{3x-y=5}\\{4x-7y=1}\end{array}\right.$得$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，再把x、y的值代入方程组$\left\{\begin{array}{l}{ax-2y=4}\\{3x-by=5}\end{array}\right.$可求出a和b的值，然后计算3a+2b．

解答 解：解方程组$\left\{\begin{array}{l}{3x-y=5}\\{4x-7y=1}\end{array}\right.$得$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，
把x=2，y=1代入方程组$\left\{\begin{array}{l}{ax-2y=4}\\{3x-by=5}\end{array}\right.$得$\left\{\begin{array}{l}{2a-2=4}\\{6-b=5}\end{array}\right.$，解得$\left\{\begin{array}{l}{a=3}\\{b=1}\end{array}\right.$，
所以3a+2b=9+2=11．
故答案为3，1，11．

点评 本题考查了二元一次方程组的解：一般地，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．