Question

10．兩位同學(xué)在解方程組$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$時(shí)，甲正確地解出方程組為$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，乙因?yàn)榘裞寫錯了而解得的解為$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，已知乙沒有再發(fā)生其他錯誤，請確定a，b，c的值．

Answer 1

分析 根據(jù)題意可知$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$是ax+by=2的解，從而可求出a與b的值，由因?yàn)?\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$是cx-7y=8的解，所以可求出c的值．

解答 解：由題意可知：$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$是cx-7y=8的解，
∴3c+14=8，
∴c=-2
由題意可知：$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$是ax+by=2的解，
∴$\left\{\begin{array}{l}{3a-2b=2}\\{-2a+2b=2}\end{array}\right.$
解得：$\left\{\begin{array}{l}{a=4}\\{b=5}\end{array}\right.$

點(diǎn)評 本題考查二元一次方程的解，解題的關(guān)鍵是熟練二元一次方程組的解法，本題屬于基礎(chǔ)題型．