方程3x+y=10的所有正整数解是（　　）

A：$\left\{\begin{array}{c}{x}_1=1\\ y_1=7\end{array}\right.$　　　　　　　

B：$\left\{\begin{array}{c}{x}_1=1\\ y_1=7\end{array}\right.$$\left\{\begin{array}{c}{x}_2=3\\ y_2=1\end{array}\right.$

C：$\left\{\begin{array}{c}{x}_2=2\\ y_2=4\end{array}\right.$$\left\{\begin{array}{c}{\mathrm{x₂}}_{\mathrm{}}=3\\ {\mathrm{y₂}}_{\mathrm{}}=1\end{array}\right.$

D：$\left\{\begin{array}{c}{x}_1=1\\ y_1=7\end{array}\right.$$\left\{\begin{array}{c}{x}_2=2\\ y_2=4\end{array}\right.$$\left\{\begin{array}{c}{x}_3=3\\ y_3=1\end{array}\right.$