Question

12．已知$\left\{\begin{array}{l}{x=3}\\{y=4}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$都是方程ax+by=22的解，試判斷：$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$是不是這個(gè)方程的解．

Answer 1

分析 根據(jù)已知條件可以列出關(guān)于a、b的方程組$\left\{\begin{array}{l}{3a+4b=22}\\{a+5b=22}\end{array}\right.$，通過解該方程組得到a、b的值；然后將$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$代入進(jìn)行驗(yàn)證即可．

解答 解：∵$\left\{\begin{array}{l}{x=3}\\{y=4}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$都是方程ax+by=22的解，
∴$\left\{\begin{array}{l}{3a+4b=22}\\{a+5b=22}\end{array}\right.$，
解得$\left\{\begin{array}{l}{a=2}\\{b=4}\end{array}\right.$．
∴該方程是2x+4y=22，即x+2y=11．
把$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$代入，得
左邊=5+2×4=13≠右邊，
∴$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$不是這個(gè)方程的解．

點(diǎn)評(píng) 本題考查了二元一次方程的解．通過解系數(shù)方程求得a、b的值是解題的關(guān)鍵．