Question

20．如果$\left\{\begin{array}{l}{x=-\frac{1}{2}}\\{y=1}\end{array}\right.$是方程組$\left\{\begin{array}{l}{ax+2y=1}\\{3x-by=2}\end{array}\right.$的解，那么a，b的值是多少？

Answer 1

分析 根據$\left\{\begin{array}{l}{x=-\frac{1}{2}}\\{y=1}\end{array}\right.$是方程組$\left\{\begin{array}{l}{ax+2y=1}\\{3x-by=2}\end{array}\right.$的解，將x、y代入原方程組即可求得a，b的值．

解答 解：∵$\left\{\begin{array}{l}{x=-\frac{1}{2}}\\{y=1}\end{array}\right.$是方程組$\left\{\begin{array}{l}{ax+2y=1}\\{3x-by=2}\end{array}\right.$的解，
∴$\left\{\begin{array}{l}{-\frac{1}{2}a+2×1=1}\\{3×（-\frac{1}{2}）-b×1=2}\end{array}\right.$，
解得a=2，b=$-\frac{7}{2}$．
即a，b的值分別是：2，$-\frac{7}{2}$．

點評 本題考查二元一次方程組的解，解題的關鍵是明確題意，將方程組的解代入原方程組求a、b的值．