Intersection of two lines with given point

Question

How to solve this? Find the line which passes through point of intersection of given two lines $\frac{x+2}{1}=\frac{y-3}{2}=\frac{z+1}{4}$ and $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$, and passes through point $(1,1,1)$

Answer 1

solve the equation System $$t-2=2s+1$$ $$2t+3=3s+2$$ $$4t-1=4s+3$$ for $s,t$