Question

8．解方程：
（1）$\left\{\begin{array}{l}{4x+y=5①}\\{3x-2y=1②}\end{array}\right.$
（2）在解方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$时，哥哥正确地解得$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，弟弟因把c写错而解得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，求a+b+c的值．

Answer 1

分析 （1）利用加减法解方程组；
（2）把把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$得：$\left\{\begin{array}{l}{3a-2b=2①}\\{3c+14=8②}\end{array}\right.$，把$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入ax+by=2得：-2a+2b=2③，①与③组成方程组$\left\{\begin{array}{l}{3a-2b=2}\\{-2a+2b=2}\end{array}\right.$解得：$\left\{\begin{array}{l}{a=4}\\{b=5}\end{array}\right.$，由②得：c=-2，即可解答．

解答 解：（1）$\left\{\begin{array}{l}{4x+y=5①}\\{3x-2y=1②}\end{array}\right.$
①×2得：8x+2y=10③，
③+②得：11x=11，
解得：x=1，
把x=1代入①得：4+y=5，
解得：y=1，
∴方程组的解是：$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$．
（2）把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$得：$\left\{\begin{array}{l}{3a-2b=2①}\\{3c+14=8②}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入ax+by=2得：-2a+2b=2③，
①与③组成方程组$\left\{\begin{array}{l}{3a-2b=2}\\{-2a+2b=2}\end{array}\right.$
解得：$\left\{\begin{array}{l}{a=4}\\{b=5}\end{array}\right.$，
由②得：c=-2，
∴a+b+c=4+5-2=7．

点评 本题考查了二元一次方程组的解，解决本题的关键是解二元一次方程组．