Allison is choosing between two rental car companies. Countrywide Auto charges $27 plus $0.27 per mile, and Smart Auto charges $45 plus $0.21 per mile.

Use the following system of equations, where y represents total cost and x represents miles, to answer the question:

y = 0.27x + 27
y = 0.21x + 45

At what point would the two lines intersect if graphed? (4 points)
(300, 108)
(108, 300)
(45, 27)
(27, 45)

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akposevictor akposevictor · Answer 1 · 2022-08-27T01:57:23+02:00

The point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

Given that:

y = total cost

x = miles

We are also given the system of linear equations that models the scenario given as:

y = 0.27x + 27 --> equation 1

y = 0.21x + 45 --> equation 2

To find the value of x, make both equations equal to each other and solve:

0.27x + 27 = 0.21x + 45

Combine like terms

0.27x - 0.21x = -27 + 45

0.06x = 18

Divide both sides by 0.06

0.06x/0.06 = 18/0.06

x = 300

To find the value of y, plug in the value of x into equation 1, and find y:

y = 0.27(300) + 27

y = 81 + 27

y = 108

Thus, the point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

Learn more about the system of linear equations on:

https://brainly.com/question/14323743

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