So I have N lines that are specified by a y-intercept and an angle, q. The constraint is that all lines must intersect. Given this constraint, I can come up with these equations:

Y = tan(q(1))X + y(1)

Y = tan(q(2))X + y(2)

...

The constraint should not contain any Y or X variables. I can easily get the constraint by hand if N = 3 or 4 but if N is greater than 4, I have some trouble. With 3 and 4 lines, when I try and solve for X, I get 2 equations and I can then set them equal to each other and get the constraint. When I have more than 4 lines, the number of equations I get that equal X is greater than 2 so I dont know how to condense that into one constraint. I need a systematic way of condensing it down that will work for any number of lines.