初中数学七年级下册(573题)
已知方程组\(\left\{ {\begin{array}{*{20}{l}} {{a_1}x + {b_1}y = {c_1}} \\ {{a_2}x + {b_2}y = {c_2}} \end{array}} \right.\)的解是\(\left\{ {\begin{array}{*{20}{l}} {x = 3} \\ {y = 4} \end{array}} \right.\),老师让同学们解方程组\(\left\{ {\begin{array}{*{20}{l}} {3{a_1}x + 4{b_1}y = 5{c_1}} \\ {3{a_2}x + 4{b_2}y = 5{c_2}} \end{array}} \right.\),小聪先觉得这道题好象条件不够,后将方程组中的两个方程两边同除以5,整理得\(\left\{ {\begin{array}{*{20}{l}} {{a_1} \cdot \frac{3}{5}x + {b_1} \cdot \frac{4}{5}y = {c_1}} \\ {{a_2} \cdot \frac{3}{5}x + {b_1} \cdot \frac{4}{5}y = {c_2}} \end{array}} \right.\),运用换元思想,得\(\left\{ {\begin{array}{*{20}{l}} {\frac{3}{5}x = 3} \\ {\frac{4}{5}y = 4} \end{array}} \right.\),所以方程组\(\left\{ {\begin{array}{*{20}{l}} {3{a_1}x + 4{b_1}y = 5{c_1}} \\ {3{a_2}x + 4{b_2}y = 5{c_2}} \end{array}} \right.\)的解为\(\left\{ {\begin{array}{*{20}{l}} {x = 5} \\ {y = 5} \end{array}} \right.\).现给出方程组\(\left\{ {\begin{array}{*{20}{l}} {{a_1}x - {b_1}y = m} \\ {{a_2}x - {b_2}y = n} \end{array}} \right.\)的解是\(\left\{ {\begin{array}{*{20}{l}} {x = 3} \\ {y = 4} \end{array}} \right.\),请你写出方程组\(\left\{ {\begin{array}{*{20}{l}} {{a_1}x - {b_1}y - 4{a_1} - 2{b_1} = 3m} \\ {{a_2}x - {b_2}y - 4{a_2} - 2{b_2} = 3n} \end{array}} \right.\)的解___.
知识点:第八章 二元一次方程组
参考答案:\(\left\{ {\begin{array}{*{20}{l}} {x = 13} \\ {y = 10} \end{array}} \right.\)