Let the three lines in two dimensions be :
a1 x + b1 y + c1 = 0
a2 x + b2 y + c2 = 0
a3 x + b3 y + c3 =0
They are concurrent if they all intersect at one point.
the point of intersection is x = (b2 c1 - b1 c2 ) / (a2 b1 - b2 a1)
y = (a1 c2 - a2 c1 ) / (a2 b1 - b2 a1)
The condition is
a1 (b2 c3 - b3 c2) - a2 ( b1 c3 - b3 c1 ) + a3 (b2 c1 - b1 c2) = 0
It is the determinant of the matrix of the coefficients of the equations of the straight lines.