Question

11．已知关于x、y的方程组$\left\{\begin{array}{l}{\frac{1}{3}a+\frac{2}{3}（b-x）=y}\\{b-x=y（a-1）}\end{array}\right.$的解是$\left\{{\begin{array}{l}{x=1}\\{y=2}\end{array}}\right.$，求a+b的值．

Answer 1

分析 把$\left\{{\begin{array}{l}{x=1}\\{y=2}\end{array}}\right.$代入方程组，得出关于a，b的方程组，再解答求出a，b的值后代入a+b解答即可．

解答 解：把$\left\{{\begin{array}{l}{x=1}\\{y=2}\end{array}}\right.$代入方程组$\left\{\begin{array}{l}{\frac{1}{3}a+\frac{2}{3}（b-x）=y}\\{b-x=y（a-1）}\end{array}\right.$，
得：$\left\{\begin{array}{l}{\frac{1}{3}a+\frac{2}{3}（b-1）=2}\\{b-1=2（a-1）}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=2}\\{b=3}\end{array}\right.$，
把a=2，b=3代入a+b=2+3=5．

点评 此题主要考查了二元一次方程组解的定义．在求解时注意用到代入消元法．