Chapter 3:  Linear Equations and Inequalities in Two Variables

 

Graph the following equations.

 

1

y

+

6

= x

y =

-3

x

+

3

9x = -21 - 3y

4x + y = -1

y =

-6

4x + y = -3

Calculate the slope of the line containing each set of points.

 

1. 
2. 
3. 

 

Find the intercepts for the following lines.

 

1. 
2. 
3. 

 

Write the equation of the following lines illustrated below.

 

 

 

 

 

 

 

 

Regina has part-time job working for a national company selling Internet subscriptions house to house.  She is paid $100 per week plus $15 for each subscription she sells. 

 

1. Complete the table below, showing her weekly pay according to the number of subscription she sells.

 

2. Using ordered pairs from the table above, graph the relationship between subscriptions sold and weekly pay for Regina.

 

3. Using variables, write an expression describing Regina’s weekly pay as it relates to the number of subscriptions she sells.

 

4. How much does Regina earn if she sells nine subscriptions in a week?

 

5. How much does she earn if she sells no subscriptions in a week?

 

6. Regina’s goal is to earn $400 next week.  How many subscriptions does she need to sell if she wants to accomplish this goal?

Chapter 4:  Systems of Linear Equations

 

Solve the following problems.

 

1. One number is twenty-eight more than three times another number. If each number were multiplied by four, their difference would be 232. What are the numbers?
2. A number is three less than four times another number. Their sum is one hundred two. What are the numbers?
3. If the larger of two numbers were decreased by three hundred forty-nine, then the two numbers would be the same. The sum of the two numbers is 735. What are the numbers?
4. The larger of two numbers is six more than six times the smaller number. The larger number is also one hundred twenty-two more than two times the smaller number. What are the numbers?
5. If Samantha were three times as old as she was five years ago, she will be sixty less than six times her current age. How old is Samantha?
6. Twenty-five years ago, Hailey was five more than one-third as old as Jason was. Today, Jason is twenty-six less than two times the age of Hailey. How old is Jason?
7. A rectangle, whose perimeter is one hundred seventy-six feet, has a length that is six feet longer than its width. What is the area of the rectangle?
8. The width of a rectangle is 4 1/6 times the size of its length. The perimeter is 24 1/9 feet. What are its dimensions?

 

Solve each system of equations using the elimination method.

1. 11x - 9y = -309 17x + 14y = -31	2. 5x - 16y = 119 x + 8y = -133	3. 19x - 2y = 614 9x - y = 291
4. 2x - 5y = -144 3x - 5y = -121	5. 5x + 6y = -3 x - 2y = -87	6. 7x + 13y = -601 8x - 3y = -169
7. 17x + 11y = -230 16x - 19y = -1009	8. 7x - 13y = -328 3x + y = 96	9. 9x + 7y = 68 12x + 7y = 107
10. 2x - 3y = -145 3x - 2y = -120	11. x - 2y = -60 5x - 12y = -346	12. 15x + y = 244 x + 9y = 320

The Department of Mathematics is trying to decide between two new copy machines.  One sells for $20,000 and costs $0.02 per copy to operate.  The other sells for $17,500, but its operating costs are $0.025 per copy.  The department decides to buy the more expensive machine.  How many copies must the department faculty and staff make before the higher price is justified?