Question

7．已知方程組$\left\{\begin{array}{l}{{a}_{1}x+_{1}y={c}_{1}}\\{{a}_{2}x+_{2}y={c}_{2}}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=6}\\{y=8}\end{array}\right.$，則方程組$\left\{\begin{array}{l}{3{a}_{1}x+4_{1}y=5{c}_{1}}\\{3{a}_{2}x+4_{2}y=5{c}_{2}}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=10}\\{y=10}\end{array}\right.$．

Answer 1

分析 根據(jù)方程組$\left\{\begin{array}{l}{{a}_{1}x+_{1}y={c}_{1}}\\{{a}_{2}x+_{2}y={c}_{2}}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=6}\\{y=8}\end{array}\right.$，可得方程組$\left\{\begin{array}{l}{3{a}_{1}x+4_{1}y=5{c}_{1}}\\{3{a}_{2}x+4_{2}y=5{c}_{2}}\end{array}\right.$中的解是$\left\{\begin{array}{l}{3x=5×6}\\{4y=5×8}\end{array}\right.$，從而求解．

解答 解：∵方程組$\left\{\begin{array}{l}{{a}_{1}x+_{1}y={c}_{1}}\\{{a}_{2}x+_{2}y={c}_{2}}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=6}\\{y=8}\end{array}\right.$，
∴方程組$\left\{\begin{array}{l}{3{a}_{1}x+4_{1}y=5{c}_{1}}\\{3{a}_{2}x+4_{2}y=5{c}_{2}}\end{array}\right.$中的解是$\left\{\begin{array}{l}{3x=5×6}\\{4y=5×8}\end{array}\right.$，
即$\left\{\begin{array}{l}{x=10}\\{y=10}\end{array}\right.$．
故答案為：$\left\{\begin{array}{l}{x=10}\\{y=10}\end{array}\right.$．

點(diǎn)評 考查了解二元一次方程組，關(guān)鍵是由方程組$\left\{\begin{array}{l}{{a}_{1}x+_{1}y={c}_{1}}\\{{a}_{2}x+_{2}y={c}_{2}}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=6}\\{y=8}\end{array}\right.$，得到方程組$\left\{\begin{array}{l}{3{a}_{1}x+4_{1}y=5{c}_{1}}\\{3{a}_{2}x+4_{2}y=5{c}_{2}}\end{array}\right.$中的解是$\left\{\begin{array}{l}{3x=5×6}\\{4y=5×8}\end{array}\right.$．