Question

20．已知方程ax+by=8的两个解为$\left\{\begin{array}{l}{x=-1}\\{y=0}\end{array}\right.$和$\left\{\begin{array}{l}{x=1}\\{y=4}\end{array}\right.$，求a+b．

Answer 1

分析 将两个解的值代入ax+by=8中，然后解出方程组即可求出a与b的值．

解答 解：将$\left\{\begin{array}{l}{x=-1}\\{y=0}\end{array}\right.$和$\left\{\begin{array}{l}{x=1}\\{y=4}\end{array}\right.$代入ax+by=8，
∴$\left\{\begin{array}{l}{-a=8}\\{a+4b=8}\end{array}\right.$
解得：$\left\{\begin{array}{l}{a=-8}\\{b=4}\end{array}\right.$
∴a+b=-4，

点评 本题考查二元一次方程的解，解题的关键是正确理解二元一次方程的解的概念，本题属于基础题型．