Here is an example: Moving company A charges a flat fee of $26 and $1 per mile to rent their van. Moving company B charges a flat fee of $10 and $5 per mile. Find the number of miles you would drive to be charged the same amount by each company.
(1) First we assign variables: let y be the total charge, and let x be the number of miles driven.
(2) For A we have y=1x+26 as the total charge is the flat fee plus the variable fee. The variable fee is found by taking the number of miles driven times the fee per mile.
For B we have y=5x+10
(3) The resulting system is
The solution of the system is the point that lies on both lines -- this is the point where the number of miles driven gives the same cost for both companies.