Question

19．已知方程组$\left\{\begin{array}{l}{ax-by=4}\\{2x+3y=4}\end{array}\right.$与$\left\{\begin{array}{l}{ax+by=2}\\{4x-3y=2}\end{array}\right.$的解相同，试求a+b的值．

Answer 1

分析 根据题意先解方程组$\left\{\begin{array}{l}{2x+3y=4}\\{4x-3y=2}\end{array}\right.$，再求a，b的值即可．

解答 解：依题意可有$\left\{\begin{array}{l}{2x+3y=4}\\{4x-3y=2}\end{array}\right.$，
解得$\left\{\begin{array}{l}{x=1}\\{y=\frac{2}{3}}\end{array}\right.$，
所以，有$\left\{\begin{array}{l}{a-\frac{2}{3}b=4}\\{a+\frac{2}{3}b=2}\end{array}\right.$，
解得$\left\{\begin{array}{l}{a=3}\\{b=-\frac{3}{2}}\end{array}\right.$，
 因此a+b=3-$\frac{3}{2}$=$\frac{3}{2}$．

点评 本题考查了二元一次方程组的解，掌握二元一次方程组的解法是解题的关键．