Question

13．解方程$\left\{\begin{array}{l}{ax-by=-2}\\{cx-7y=8}\end{array}\right.$时，甲正确解得$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，乙因看错了c而解得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，则a+b-c=7．

Answer 1

分析 将$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入cx-7y=8，可解出c的值，将$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入ax+by=2，联立可解出a、b的值，继而代入求解代数式的值．

解答 解：将$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入cx-7y=8，可得：3c=-6，
解得：c=-2，
由题意可得$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$、$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$均满足ax+by=2，
则$\left\{\begin{array}{l}{3a-2b=2}\\{-2a+2b=2}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=4}\\{b=5}\end{array}\right.$，
则a+b-c=4+5-2=7，
故答案为：7．

点评 本题考查了二元一次方程组的解，能使方程组中每个方程的左右两边相等的未知数的值即是方程组的解．