Write both lines in a common form, such as:
(a_1x + b_1y = c_1)
(a_2x + b_2y = c_2)
Solve the system of two equations for (x) and (y)
Use substitution, elimination, or matrix methods
If the determinant (a_1b_2 – a_2b_1 neq 0), the lines intersect at one point
If the determinant (a_1b_2 – a_2b_1 = 0) and the equations are not proportional, the lines are parallel and do not intersect
If the equations are proportional, the lines are the same line and intersect at infinitely many points
The intersection point is the pair ((x, y)) that satisfies both equations