College Algebra (TUTOR DANIEL ONLY)

1.      What are the 3 methods for solving systems of equations? Which one do you prefer and why?

2.      Describe a consistent system.

3.      Describe an inconsistent system.

4.      Describe a dependent system.

Solve the following systems of equations using the graphing method. 

What type of system is it? Name the solution if there is one.

1. x + y = 5
   -x + y = 3

2. 2x – 2y = 8
   x – y = 4

3. 3x – y = -2
   3x – y = 4

4. y = 6
   x = -3

   Solve the following systems of equations using the substitution method. 

   What type of system is it? Name the solution if there is one.

1. x = 6y + 2
   3x – 18y = 4

2. x – y = 3
   x + 3y = 6

3. y = -2x
   4x – 3y = 12

4. 2x – 5y = 15
   x – 7y = 3

   Solve the following systems of equations using the addition (elimination) method. 

   What type of system is it? Name the solution if there is one.

1. x + y = 6
   x – y = 4

2. -2x + 3y = 5
   2x – y = 1

3. 5x + y = 2
   3x + y = 1

4. 5x = 20 + y
   16 = 3y + 4x

   Solve the following systems of inequalities using the graphing method. 

   Shade the solution set.

1. x + y > 4
   y + 3x < 6

2. x ≥ 5
   y < 3

3. 3x – 2y > 8
   -2y + 3x < 12

4. 2x + y < 8
   x ≥ 4

____________________________________________________________________________

Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.

1.      Describe the three types of solutions systems of equations have when graphed.

2.      The sum of two numbers is 30 and their difference is 2. Find the two numbers by writing and solving a system of equations.

3.      Two apples and three pears cost $3.45. Three apples and five pears cost $5.55. Find the cost of each type of fruit.

4.      Mary has a total of $5,000 invested in two accounts. One account pays 5% and the other 8%. Her interest in the first year was $331. Write and solve a system of equations to find out how much she has invested in both accounts.

5.      Terry is mailing two boxes. Together they weigh 21 lbs. If the smaller box is 5 lbs. less than the larger one, how much does each box weigh? Write and solve an equation that models this scenario.

6.      The length of a pool is 3 feet more than twice its width. If the perimeter of the pool is 72 feet, find the dimensions of the pool by writing and solving a system of equations.

7.      A desk and a chair cost $200 as a set. If the desk costs four times more than the chair, how much does each one cost? Write and solve using a system of equations.

8.      Rachel has 15 coins with a value of $2.85. If the coins are either dimes or quarters, how many of each coin does she have? Write and solve using a system of equations.

9.      A music concert was attended by 450 people. Adult tickets sold for $70 and children’s tickets for $40. If total sales were $27,750, how many of each ticket was sold?

10.     A party planner can spend a maximum of $5,000 on food. If the chicken dinner (x) costs $20 and the steak dinner (y) costs $25, make a graph of the region that shows the possibilities for the number of chicken and steak dinners that can be purchased while still staying within budget. Shade the solution set.

__________________________________________________________________________________________

Discussion:

What are the three methods for solving systems of equations?  Do they all produce the same answer?  Which method do you prefer to use and why?

Create 1 system of equations and ask your peers to solve it using 1 of the 3 methods.  Return to the discussion to check your peers’ understanding and offer help as needed.  Be sure to post your answer at the close of the module.