Systems of Equations Review

Solving Systems of Equations Using the Addition/Elimination Method

This is your review material for you test. You need to complete every problem and check each one to make sure that you are ready for Friday. Every question can be checked using the plug in method. You test will require you to do the following tasks

  1. Use graphing to find an intersection point (with and without a calculator)
  2. Use substitution to find the solution to a system (see last quiz)
  3. Use elimination to find the solution to a system
  4. Use the correct (easiest) method to find the solution to a system
  5. Read, comprehend, and solve real world problems.

A. SOLVE THE FOLLOWING SYSTEMS OF EQUATIONS USING THE ADDITION METHOD, multiply one equation if necessary.

1.x + y = 12.2x + y = -3

-x + y = 53x - y = -12

3.2x - y = 84.2x + 2y = 4

x + 3y = 4-x + 2y = 4

5.3x + 4y = 256.x + y = 5

3x - 3y = -3 x + y = -5

7.3x + 4y = 108. x - 5y = 59. x - 2y = -2

6x - 4y = 83x + y = 31-2x + 4y = 4

B. SOLVE, MULTIPLYING Both Equations TO ELIMINATE ONE VARIABLE

1. 5x + 2y = 82. 3x + 2y = 8

3x - 5y = 11 4x - 3y = -12

3. 4x + 3y = 14. 2x + 5y = 11

5x - 4y = 9 3x + 8y = 16

Of the three methods for solving systems of equations (graphing, substitution, addition/elimination) which method would work best in each of the following problems? Explain your choice!! Solve.

1. y = 2x – 52. 5x – 4y = 15

4y + 3x = 13 2x + 5y = 6

3. y = x – 54. 2x = 3y + 6

y = -x + 1 5x – 2y = 15

Answers for 1-4 above (solving systems):

1) (3,1) 2) (3,0) 3) (6,-1) 4) (3,0)

Combined Practice

Solving Systems of Equations

Solve the following systems of equations using the method of your choice. You may use as many or few of the graphs as you choose.

1. y + 2x = 5

3x – 2y = 4

2. y = x - 5

y = -2x + 4

3. 3x - 4y = 12

5x + 4y = -12

4. y = x + 1

2x - 5y = 4

5. y = 4x + 1

2x + 2y = 7

Answers: 1. ( 2,1 ) 2. ( 3, -2 ) 3. ( 0, -3 ) 4. ( -3, -2 ) 5.

Modeling Real Life Problems

Solve the following solutions using two unknowns. Before working each problem analyze the information and organize it in a chart or using some type of symbolism in order to be able to set up two separate equations using x and y as the unknowns. Then solve the equations by the method of choice learned earlier in this unit.

  1. The sum of two numbers is 41. The larger number is 1 less than twice the smaller. Find the numbers.
  1. There are two numbers whose sum is 53. Three times the smaller is equal to 19 more than the larger number. What are the numbers?
  1. Ezekiel has some coins in his pocket consisting of dimes, nickels, and pennies. He has two more nickels than dimes and three times as many pennies as nickels. How many of each kind of coin does he have if the total value is 52 cents?
  1. A man is four times as old as his son. In 3 years the father will be three times as old as his son. How old is each now?
  1. Tickets for the school play sold at $2 each for adults and 75 cents for students. If there were four times as many adult tickets sold as students tickets, and the total receipts were $1750, how many adult and how many student tickets were sold?
  1. The length of a rectangle is 5 feet more than twice the width. The perimeter is 28 feet. Find the length and width of the rectangle.

7. The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

8. The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

9. The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

10. Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?