System of Linear Equations Project

By: Samantha Paxton

word problem

You got your first job and decided it is time to buy a car. You are debating between two cars, a Volkswagen Beetle 1.8T or a 2015 Jeep Wrangler Sport 4x4. The Volkswagen Beetle costs $24, 425 and has 33 miles per gallon and the Jeep Wrangler costs $23,990 with 21 miles per gallon. Assuming gas is $2.25 per gallon, what car would be the best buy for long term? What car would be the better buy for short term? What are the independent and dependent variables?

system of linear equations and graph

System of linear equations for the Volkswagen Beetle-


y = .07 x + 24,425


System of linear equations for the 2015 Jeep Wrangler-


y= .11 x + 23,990

Check Graph with Elimination

Y=.07x+24,425



Subtract .07 from both sides giving you:


-.07x + y= 24,425




Y=.11x+23,990


Subtract .11 from both sides giving you:



-.11x + y = 23,990




Now, multiply -.11x + y = 23,990 by -1 which would give you: .11x - y = -23,900. And you are ready to eliminate!


-.07x + y = 24,425

.11x - y = - 23,990


y-y= 0, so you can now get rid if the y values, add the x values, and subtract the 24,425- 23,990, which will give you the equation:


.04x=435


You can now divide .04 by both sides giving you:


X = 10, 875


You can now substitute the x value we just found into one of the equations to find the y value.



y = .07 (10,875) + 24,425

y = 25,186.25



This means that at 10,875 miles, the two cars' prices will be equivalent at $25,186.25.

What Car is the Better Buy?

A car for the better buy varies for the person. How long are you planning to keep the car, if you have a family, where you live. The Volkswagen Beetle 1.8T would probably be the best buy for me. All though in the beginning, the Jeep is cheaper, after you drive for about 1 year (or 10, 875 miles) the Jeep would start to cost you more money.