casey is deciding which of two landscapers to hire. each landscaper charges an hourly rate plus a fee for…
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?\none landscaper charges $20 for 5 hours of work.\none landscapers hourly rate is $15 lower than the other landscapers.\nboth landscapers charge the same hourly rate and the same fee per job.\nboth landscapers charge the same hourly rate, but not the same fee per job.
Answer
Explanation:
Step1: Analyze equation result
The equation $5 = 20$ is a false - statement. In the context of solving a system of linear equations by substitution, when we get a false - statement like this, it means the system of equations has no solution.
Step2: Relate to landscaper costs
Let the cost equations for the two landscapers be $C_1 = r_1h + f_1$ and $C_2 = r_2h + f_2$, where $r$ is the hourly rate and $f$ is the fee per job. A no - solution system implies that the lines representing the cost equations are parallel. Parallel lines in the cost - equation context mean the hourly rates ($r_1$ and $r_2$) are equal (same slope), but the y - intercepts (the fee per job $f_1$ and $f_2$) are different.
Answer:
D. Both landscapers charge the same hourly rate, but not the same fee per job.