does the point $\displaystyle (4,5,6)$ lie in the plane $\displaystyle (x,y,z)=(4,1,6)+p(3,-2,1)+q(-6,6,-1)

$

i started by writing the parametric equations

$\displaystyle x=4+3p-6q$

$\displaystyle y=1-2p+6q$

$\displaystyle z=6+p-q$

subbing in$\displaystyle (4,5,6)$ into the corresponding equations

$\displaystyle 4=4+3p-6q$

$\displaystyle 5=1-2p+6q$

$\displaystyle 6=6+p-q$

simplifying gives

$\displaystyle 0=3p-6q$

$\displaystyle 4=-2p+6q$

$\displaystyle 0=p-q$ thus $\displaystyle p=q$

what do i do now? i know i need to figure out p and q i just cant figure it out