jmc

Simplify both equations by dividing by 3: $$\begin{array}{rl}4x+7y& =5\\ 7x+4y& =17.\end{array}$$ We solve this system using the elimination method. Multiply the first equation by 7 and the second equation by $-4$ to obtain $$\begin{array}{rl}28x+49y& =35\\ -28x-16y& =-68.\end{array}$$ Adding the equations gives $33y=-33$, so $y=-1$. Substituting $y=-1$ into either equation and solving, we get $x=3$. Therefore, $(x,y)=\boxed{(3,-1)}$.