Решите систему3x*7y=63 3x+7y=16

[latex] \left \{ {{3x*7y=63} \atop {3x+7y=16}} \right. [/latex] Делаем замену: 3x=m, 7y=n и получаем систему уравнений [latex] \left \{ {{mn=63} \atop {m+n=16}} \right \rightarrow m=16-n; \quad (16-n)*n=63; \\ n^2-16n+63=0; \quad D=16^2-4*1*63=4; n_{1,2}= \frac{16\mp 2}{2}; \\ n_1=7 \rightarrow 7y_1=7; \quad y_1=1; \\ n_2=9 \rightarrow 7y_2=9; \quad y_2= \frac{9}{7} [/latex] [latex]3x+7y=16 \rightarrow x= \frac{16-7y}{3}; \\ x_1= \frac{16-7*1}{3}=3; \quad x_2= \frac{16- 7* \frac{9}{7} }{3}= \frac{7}{3} \\ \left \{ {{x_1=3} \atop {y_1=1}} \right; \quad \left \{ {{x_2=7/3} \atop {y_2=9/7}} \right. [/latex]