Final answer:
To find the intersection point of the given line and plane equations, we need to solve the system of equations formed by them.
Step-by-step explanation:
To find the point at which the line 5x - y + 3z = 1 intersects the plane 4x + 14y - z = 0, we need to solve the system of equations formed by these two equations. First, we can rewrite the equations in standard form:
5x - y + 3z = 1
4x + 14y - z = 0
Next, we can use the method of substitution or elimination to solve the system and find the values of x, y, and z that satisfy both equations.