# · How do you write a system of linear equations in two variables? Explain this in words and by using mathematical notation in an equation.

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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

`y=x+26`

`y=5x+10`

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.