# Linear equations and linear systems

1. Find the intercept, then graph in a document.

Y = -40 + 5x

2. On February 10th, Oscar rented a Chevy Trailblazer with a full tank of gas and 13,091 miles on the odometer. On February 12th he returned the vehicle with 13,322 on the odometer. The rental agency charged $92.00 and needed 14 gallons of gas to fill the tank. Please give an explanation for the answers to the following questions.

a) Find the SUV'S rate of gas consumption in miles per gallon.

b) Find the average cost of the rental in dollars per day.

c) Find the average rate of travel, in miles per day.

d) Find the rental rate in cents per mile.

3. Solve using the elimination method and explain the answer.

2x/3 + 3y/4 = 11/12

x/3 + 7y/18 = 1/2

https://brainmass.com/math/linear-algebra/linear-equations-linear-systems-312098

## SOLUTION This solution is **FREE** courtesy of BrainMass!

1. Find the intercept then graph in a document

Y=-40+5x

There are two types of intercepts. There are x intercepts and y intercepts. These are the points where the graph crosses the x axis and the y axis respectively. When a graph crosses the y axis, the value of the x variable will be 0 at that point. When the graph crosses the x axis, the value of the y variable will be 0. You can find the x and y intercepts by substituting 0 in place of either x or y and then solving the equation for the other variable. To find the y intercept of this equation, put 0 in place of x to get y = -40 + 5 * 0 = -40 so the y intercept is -40. To find the x intercept, put 0 in place of y to get 0 = -40 + 5x. Add 40 to both sides of the equation to get 40 = 5x and then divide both sides by 5 to get the final answer of x = 8 so the x intercept is 8.

2. SUV RENTALS. On February 10th, Oscar rented a Chevy Trailblazer with a full tank of gas and 13,091 mi on the odometer. On February 12th he returned the vehicle with 13,322 on the odometer. The rental agency charged $92.00 and needed 14 gallons of gas to fill the tank. Please give an explanation for the answers to the following questions

a) Find the SUV'S rate of gas consumption in miles per gallon.

The total miles travelled is 13,322 - 13,091 = 231. The number of gallons of gas used was 14. Divide the two to get 231 / 14 = 16.5 miles per gallon.

b) Find the average cost of the rental in dollars per day.

The total cost of the rental was $92 and the rental lasted for 2 days. Divide the two to get 92 / 2 = 46. So the cost per day was $46.

c) Find the average rate of travel, in miles per day.

The total number of miles travelled was 231 over a period of two days. Divide the two to get 231 / 2 = 115.5 miles per day.

d) Find the rental rate in cents per mile.

The rental rate in dollars per mile is $92 / 231 miles= 0.398 dollars per mile. To find the number cents per mile, remember that there are 100 cents per $1 so we will multiply this by 100. This is 100 * 0.398 = 39.8. So, the cost is 39.8 cents per mile.

3. Solve using the elimination method and explain answer submitted.

2x/3 + 3y/4 = 11/12

x/3 + 7y/18 = 1/2

We want to eliminate one of the variables. It will be easiest to eliminate x in these two equations because the first equations x value is twice the second equations x value. If you multiply each number in the second equation by -2, the second equation becomes -2x/3 - 14y/18 = -2/2. Combine this with the first equation which is 2x/3 + 3y/4 = 11/12. If you add the two equations together now, that is, if you add the x and y parts together and then you add the right hand side of the equations, you get 0x + (3/4 - 14/18)y = 11/12 - 2/2. You will need to find a common denominator to add on the two parts which gives (27/36 - 28/36)y = 11/12 - 12/12 or -1/36 y = -1/12. Now, multiply both sides by -36 to get y = -36 / -12 = 3. So, y = 3. Now you can find x by replacing y with 3 in one of the equations. Choosing the first equation gives you 2/3 x + (3*3)/4 = 11/12. Times the threes together to get 2/3 x + 9/4 = 11/12. Next, subtract 9/4 from both sides to get 2/3 x = 11/12 - 9/4. Get another common denominator which will be 2/3 x = 11/12 - 27/12 = -16/12. So you have 2/3 x = -16/12. Multiply both sides by 3/2 to get x = 3/2 * -16/12 = -48 / 24 = -2. So, x = -2. The answer to this system of equations using the elimination method is (-2,3).

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