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Intersection of Lines
 
Question: How do we find the point of intersection of two lines? For example:
 
 
Yours Truly answers: Generally, we will first try to eliminate  y  in the equations.
 
Step 1. Solve  2x + 4y = 11   for  y.

 

Step 2. Solve  –5x + 3y = 5   for  y.

Step 3. Equate (1) and (2) to eliminate  y.

NOTE: In the last step, subsitutution was made back into (1). But, (2) can be used instead. Either way yields the same value for  y.

Step 4. Therefore, the coordinates of the point of intersection are given by
 
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