Line AB, with equation: 3x + 2y - 1 = 0, intersects line CD, with equation 4x - 6y -10 = 0. Find the point, P, where the two lines intersect.

Let eqn. 1 be: 3x + 2y - 1 = 0  & Let eqn. 2 be: 4x - 6y -10 = 0

Multiply eqn. 1 by a factor of 3, and add the two eqautions together. (This eliminates y from the equation)

This gives: 9x + 6y - 3 = 0

+                4x - 6y - 10 =0

This gives the equation: 13x - 13 = 0, so 13x = 13, and therefore x =1. 

Substitute this value of x into either eqn. 1 or eqn. 2. (I will use eqn. 1 for this example)  3(1) + 2y - 1 = 0. This can be rearranged to give 2y = -2, and hence y = -1.

Therefore, point P is at (1, -1).