From Mechanics

\displaystyle \begin{align} & 2m(8\mathbf{i}+7\mathbf{j})+m(U\mathbf{i}+V\mathbf{j})=2m(5\mathbf{i})+m(2\mathbf{j}) \\ & U\mathbf{i}+V\mathbf{j}=(10-16)\mathbf{i}+(2-14)\mathbf{j} \\ & =-6\mathbf{i}-12\mathbf{j} \\ & U=-6 \ \text{ m}{{\text{s}}^{-1}}\text{ and }V=-12 \ \text{ m}{{\text{s}}^{-1}} \end{align}