HELP WITH VECTORS & PLANES IN 3D

Find the y-intercept of the plane: (x,y,z) = (5,-1,0) + t(1,-1,3) + r(-3,4,1).
Please help :'(

The y-intercept is at (0, 5 1/2, 0). (Answer)

For x: 5 + t - 3r = 0
For z: 1 + 3t + r = 0

Solve these two equations to get t = -1/2 and r = 3/2. Then substitute to get

(x, y, z) = (5, -1, 0) - 1/2 (1, -1, 3) + 3/2 (-3, 4, 1) = (0, 5 1/2, 0)