Let $\overline{a}$ , $\overline{b }$be two noncollinear vectors. If $\overline{OA}=(\mathrm{x}+4\mathrm{y})\overline{a}+(2\mathrm{x}+\mathrm{y}+1)\overline{b}, \overline{OB}=(\mathrm{y}-2\mathrm{x}+2)\overline{a}+(2\mathrm{x}-3\mathrm{y}-1)\overline{b}$ and $3\overline{OA}=2\overline{OB}$ then $(x,y) =$

$3\left\{\right(x+4y)\overline{a}+(2x+y+1\left)\overline{b}\right\}$

$=2\left\{\right(y-2x+2)\overline{a}+(2x-3y-1\left)\overline{b}\right\}$

Comparing the coefficients of $\overline{a,}$ $\overline{b}$ on both sides we 

$\text{ get }\Rightarrow 7x+10y=4\dots \left(1\right)\Rightarrow 2x+9y=-5\dots \left(2\right)$

Solving equation $\left(1\right)$ and $\left(2\right) (x, y) = (2, –1)$