The point of intersection of two lines and is given by

where

.

To proof this formula we have the given equations of straight lines

Solving above equations by simultaneous method.

Multiplying equation (i) by

, we have

Multiplying equation (ii) by

, we have

Now subtracting (iv) from equation (iii), we get

Multiplying equation (i) by

, we have

Multiplying equation (ii) by

, we have

Now subtracting (vi) from equation (v), we get

This shows that point of intersection is

Note: If

, then lines (i) and (ii) will have no common point and therefore, these will be parallel lines.

Now

This is the condition for two lines (i) and (ii) to be parallel lines.

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