$\left\{u+v+w\=t\,4u-v\=-t\,2u+2v-3w\=0\right\}$

$\left\{4u-v\=-t\,u\+v\+w\=t\,2u\+2v-3w\=0\right\}$

$\mathrm{solve}\left(\,\left\{u\,v\,w\right\}\right)$

$\left\{u\=-\frac{2}{25}t\,v\=\frac{17}{25}t\,w\=\frac{2}{5}t\right\}$