Question

16．已知$\left\{\begin{array}{l}{x=a}\\{y=b}\end{array}\right.$是方程组$\left\{\begin{array}{l}{-3x+y=2}\\{4x+y=5}\end{array}\right.$的解，则a+2b的值为7．

Answer 1

分析 把$\left\{\begin{array}{l}{x=a}\\{y=b}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{-3x+y=2}\\{4x+y=5}\end{array}\right.$中，得出关于a，b的值，再计算即可．

解答 解：把$\left\{\begin{array}{l}{x=a}\\{y=b}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{-3x+y=2}\\{4x+y=5}\end{array}\right.$中，可得：
$\left\{\begin{array}{l}{-3a+b=2}\\{4a+b=5}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=\frac{3}{7}}\\{b=\frac{23}{7}}\end{array}\right.$，
把$\left\{\begin{array}{l}{a=\frac{3}{7}}\\{b=\frac{23}{7}}\end{array}\right.$代入a+2b=7，
故答案为：7．

点评 本题主要考查了方程组的解的定义：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．