Let `a_1x + b_1y + c_1 = 0` and `a_2x + b_2y + c_2 = 0` be two non-parallel lines. If
`(x_1, y_1)` be the co-ordinates of their point of intersection,

then `a_1x_ 1 + b_1y_1 + c_1 = 0`

and `a_2x_1 + b_2y_1 + c_2 = 0`

Solving these two by cross multiplication, then

`x_1/(b_1c_2 - b_2c_1) = y_1/(c_1a_2-c_2a_1) = 1/(a_1b_2- a_2b_1)`

we get` (x_1, y_1) = ((b_1c_2 - b_2c_1)/(a_1b_2- a_2b_1) ,(c_1a_2-c_2a_1)/(a_1b_2- a_2b_1) )`

`=(|(b_1,b_2),(c_1,c_2)|/|(a_1,a_2),(b_1,b_2)| , |(c_1,c_2),(a_1,a_2)|/|(a_1,a_2),(b_1,b_2)|)`

NOTE `=> ` Here line are not parallel , they unequal slopes , then `a_1b_2-a_2b_1 ne 0`

`text (Funda :)`
In solving numerical questions, we should not be remember the co-ordinates `(x_1, y_1)` given above, but we solve the equations directly.