# If $\overrightarrow {\alpha}=(x+4y)\overrightarrow a+(2x+y+1)\overrightarrow b\:\:and\:\:\overrightarrow {\beta}=(y-2x+2)\overrightarrow a+(2x-3y-1)\overrightarrow b$ where $\overrightarrow a\:\:\overrightarrow b$ are non zero non collinear and if $3\overrightarrow {\alpha}=2\overrightarrow {\beta}$, then $(x,y)=?$

Given: $3\overrightarrow {\alpha}=2\overrightarrow {\beta}$
$\Rightarrow\:3x+12y=2y-4x+4\:\:and\:\:6x+3y+3=4x-6y-2$
$\Rightarrow\:7x+10y-4=0\:\:and\:\:2x+9y+5=0$
Solving which we get $y=-1\:\:and\:\:x=2$
$\therefore\:(x,y)=(2,-1)$