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Algebra

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1. Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
5x - 2y = -1
x + 4y = 35

2. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-4x + 9y = 20
-2x - 2y = 10

3. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.
The sum of two numbers is 54, and their difference is nine more than the smaller number. Find the numbers.

4. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $135.00 for 3 days and 300 miles, while Mary was charged $250.00 for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

5. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
An orchard operator must dilute 11 quarts of a 60%-insecticide solution by adding water. How many quarts of water should be added to get a mixture that is 2% insecticide?

6. Given the pair of linear equations in two variables:
? Find the x- and y-intercepts (if any) for each line. Show your work.
? Plot those intercepts, and graph the two lines on the same chart.
? Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). Show your work.
x + 8y = 8
9x - 5y = -5

7. Given the pair of linear equations in two variables:
? Find the x- and y-intercepts (if any) for each line. Show your work.
? Plot those intercepts, and graph the two lines on the same chart.
? Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). Show your work.
-5x + 4y = 8
15x - 12y = 24

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Solution Summary

This solution is comprised of detailed step-by-step calculation of the given problems related to Algebra. This solution provides students with a clear perspective of solving linear equations in Algebra.

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Algebra Homework Help 5: To show your work, you will need to include the algebra used to compute the solution to any equations.

1. The following graph shows how a 4-color web printing press depreciates from the year 2006 to the year 2010. It was purchased new in the year 2006; therefore x = 0 represents the year 2006.
X - axis (horizontal) = years starting from 0 = 2006 and increasing by 0.5 years
Y - axis (vertical) = price in $ amounts

a) List the coordinates of any two points on the graph in (x, y) form.
(___, ___),(___, ___)

b) Find the slope of this line:

c) Find the equation of this line in slope-intercept form.

d) If trend for the depreciation of the press continued, what would be its value in the year 2015? Show how you obtained your answer using the equation you found in part c).

2. Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm.
a) Set up an equation for the perimeter involving only W, the width of the rectangle.

b) Solve this equation algebraically to find the length of the rectangle. Find the width as well.
Length ______, Width ______

3) A temporary agency offers two payment options for administrative help:
Option1: $25 daily fee plus $10/hour; or
Option 2: No daily fee but $15/hour
Let x = total hours worked.

a) Write a mathematical model representing the total temp cost, C, for a four-day temporary administrative assistant in terms of x for the following:
Option 1: C=_________________
Option 2: C=_________________

b) How many total hours would the temp need to work in the four day period for the cost of option 1 to be less than option 2. Set up an inequality and show your work algebraically using the information in part a. Don't forget about the daily fee in Option 1 (it's a four day proposition!). Do not assume an eight our workday. Any number of hours per day is possible.

4) Use the graph of y = 7 - 6x - x2 to answer the following:
a) Without solving the equation (or factoring), determine the solutions to the equation 7 - 6x - x2 = 0 using only the graph. Explain how you obtain your answer(s) by looking at the graph:

b) Does this function have a maximum or a minimum? Explain how you obtain your answer by looking at the graph:

c) What is the equation of the line (axis) of symmetry for this graph?

d) What are the coordinates of the vertex in (x, y) form?

5) The profit function for the Recklus Hang gliding Service is P(x) = -0.4x2 + fx - m, where f represents the set up fee for a customer's daily excursion and m represents the monthly hanger rental. Also, P represents the monthly profit in dollars of the small business where x is the number of flight excursions facilitated in that month.

a) If $40 is charged for a set up fee, and the monthly hanger rental is $800; write an equation for the profit, P, in terms of x.

b) How much is the profit when 30 flight excursions are sold in a month?

c) How many flight excursions must be sold in order to maximize the profit? Show your work algebraically. Trial and error is not an appropriate method of solution - use methods taught in class.

d) What is the maximum profit?

6. Graph the equations on the same graph by completing the tables and plotting the points. You may use Excel or another web-based graphing utility.

a) y = 2x - 5
Use the table; find at least 3 points using any values for x.

x y
-1
1
3

b) y = 3x - x2
Use the values of x provided in the table.
x y
-1
0
1
2
3
4

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