Casey is deciding which of two landscapers to hire. each landscaper charges an hourly rate plus a fee for each job.

casey correctly wrote and solved a system of linear equations by substitution. in his work, he substituted an expression for one variable and solved for the other. this resulted in the equation 5 = 20. what can casey conclude?

The conclusion is that the system does not have a solution. This is that the equations written do not have an intersection point, they represent parallel lines and, for any x value, one line is always over the other.

In terms of the landscapers charges, it means that the two landscapers have the same hourly rate (the slope of the lines) but different fees..

For example imagine one landscapers charges $0.5 the hour plus a fixed $5 fee

The correspondan equation would be: y = 0.5x + 5

If the other charges $0.5 the hour and a fixed $20 fee. the correspondant equation would be y = 0.5 x + 20

When you try to solve the system you get:

0.5x + 5 = 0.5x + 20

You can remove the 0.5x terms because they appear in the two sides, then

5 = 20.

Which means that the two costs will never be equal.

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