# System of Linear Equations Project

## 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.