When two things intersect, their components are equal. You want to find where x1 = x2, y1 = y2, and z1 = z2
This gives you a system of 3 equations, which you can use any two of to solve (If there is a solution. There's no guarantee that two lines will intersect! You'll have to check your results to make sure both lines completely meet.)
-2t = -9 + 5s
1 + 2t = 5s
3t = 2 + 4s
Adding the first two equations makes it easy to solve for s.