Question

10．解方程组$\left\{\begin{array}{l}{ax+by=1}\\{cx+dy=-1}\end{array}\right.$时，甲把c看错了，得到$\left\{\begin{array}{l}{x=-\frac{19}{6}}\\{y=-\frac{3}{2}}\end{array}\right.$，乙把d看错了，得到$\left\{\begin{array}{l}{x=-6}\\{y=-\frac{19}{7}}\end{array}\right.$，求a，b的值．

Answer 1

分析 直接根据题意把$\left\{\begin{array}{l}{x=-\frac{19}{6}}\\{y=-\frac{3}{2}}\end{array}\right.$，$\left\{\begin{array}{l}{x=-6}\\{y=-\frac{19}{7}}\end{array}\right.$，代入ax+by=1，进而得出答案．

解答 解：由题意可得：$\left\{\begin{array}{l}{-\frac{19}{6}a-\frac{3}{2}b=1}\\{-6a-\frac{19}{7}b=1}\end{array}\right.$
整理得：$\left\{\begin{array}{l}{19a+9b=-6①}\\{42a+19b=-7②}\end{array}\right.$，
由①得：a=$\frac{-6-9b}{19}$，
把a的值代入②得：
b=$\frac{119}{3}$，
可得a=-$\frac{363}{19}$．

点评 此题主要考查了二元一次方程组的解法，正确得出二元一次方程组是解题关键．