Expert: Richard J. Raridon - 2/6/2012

Question
1. Solve the system, using substitution. Write the solution as an ordered pair.
x = 2y - 2 and 3x - y = 14
A. (6, 4)
B. (4, 6)
C. (1, 0)
D. (0, 1)
E. no solution

2. Solve the system, using substitution.
3a - b = 11 and 2a + 3b = 0
  A.(3, 2)
  B.(3, -2)
  C.(-3, 2)
  D.(-3, -2)
  E.no solution


3. Solve the system, using substitution. Write the solution as an ordered pair (m, n).
2m - 3n = 6 and m = 3 - 2n
  A.(6, 2)
  B.(3, 0)
  C.(-3, -4)
  D.(0, 2)
  E.no solution


4. Solve the system, using substitution.
4x + y = 4 and y = 4 - 4x
  A.no solution
  B.infinitely many solutions


5. Solve the system, using substitution.
y = 1 - 5x and 5x + y = 8
  A.no solution
  B.infinitely many solutions


6. Solve the system by using elimination or elimination with multiplication.
2x + 3y = 12 and 3x + 2y = 13
  A.(3, 2)
  B.(-3, 2)
  C.(-3, -2)
  D.no solution
  E.infinitely many solutions


7. Solve the system by using elimination or elimination with multiplication.(Type the steps and the correct solution) One point for the steps and one point for the correct solution.
3x + 4y = -2 and 2x - 3y = 10

8. Solve the system by using elimination or elimination with multiplication. Write the solution as an ordered pair (a, b).
a - b = -5 and a + 2b = 1
  A.(3, 2)
  B.(3, -2)
  C.(-3, -2)
  D.(-3, 2)
  E.no solution


9. Solve the system by using elimination or elimination with multiplication.
x + y = 16 and x + y = -2
  A.(8, 8)
  B.(-2, 4)
  C.(-1, -1)
  D.no solution
  E.infinitely many solutions


10. Solve the system by using elimination or elimination with multiplication.
5x - 3y = 29 and x - 4y = 16
  A.(4, 3)
  B.(-4, 3)
  C.(4, -3)
  D.no solution
  E.infinitely many solutions


11. Solve the system by using elimination or elimination with multiplication. *One point for the steps and one point for the correct solution*
x - y = 3 and x + y = 7

12. Solve the system by using elimination or elimination with multiplication.
3x - 2y = 9 and -3x + 2y = -9
  A.(3, 0)
  B.(5, 6)
  C.(1, -3)
  D.no solution
  E.infinitely many solutions

13. Solve the following system using substitution or elimination: The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Be sure to show all work.

14. Write the solution to this problem as an ordered pair:  To skate at Roller Heaven, each person must pay a monthly membership fee (m) and a fee for each session (f). In January, Art attended 5 sessions and paid $25 in all. In July, he attended 10 sessions, and he paid $40 in all. How much is the membership fee and how much are the session?

15. Solve the following problem using substitution or elimination: The sum of two numbers is 170 and their difference is 26.  Be sure to show all work.


16. Write a system of two equations with the variables m and f in each to represent the following problem: To skate at Roller Heaven, each person must pay a monthly membership fee (m) and a fee for each session (f). In January, Art attended 5 sessions and paid $25 in all. In July, he attended 10 sessions, and he paid $40 in all.

17. Write a system of two equations using x and y for the following problem: The sum of two numbers is 170 and their difference is 26. Find the two numbers.

18. Solve the following problem using substitution or elimination:  To skate at Roller Heaven, each person must pay a monthly membership fee (m) and a fee for each session (f). In January, Art attended 5 sessions and paid $25 in all. In July, he attended 10 sessions, and he paid $40 in all. How much is the membership fee and how much are the session?  Be sure to show all work.

19. Write the solution to the following problem as an ordered pair:  The sum of two numbers is 170 and their difference is 26.


20. Write two equations which represent the following two sentences: The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x.


21. Write the solution for the following problem as an ordered pair: The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Be sure to show all work.


22. Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use?


23. Before beginning this discussion thread assignment, read over the problems you’ve studied so far in the Solving Systems unit. Then make up a problem involving two values which must be solved. Make sure that you know how to solve the problem you create. Other students will post responses to your problem and you must be able to answer the other students.  Review the problems that other students have posted. Select one and solve it. After you’ve completed these steps, post a response to the discussion thread that includes the following:
The problem you created. Remember, the problem must involve two values which must be solved. You don’t need to show the solution to your problem, but make sure you do know how to solve it.
Your answer to another student’s problem. Make sure you tell in your post what the original problem was that you are answering.
Other students will be posting responses to your problem. Be sure to respond to any answers you get from other students.
Have fun! Student: 5x+3y = -9 3x-5y=-9. Reply to that

24. Solve the system of equations: what is the y-value in the solution?
3x - 5y = -16 and 2x + 5y = 31
  A.5
  B.3
  C.2
  D.4


25.Solve the system of equations.
5x - y = 3 and -10x + 2y = -6
  A.(0, -3)
  B.(-3, 0)
  C.(3, 12)
  D.no solution
  E.infinitely many solutions


26. Choose the correct first step(s) to solve the system using elimination.
4x + 7y = 6 and 6x + y = 2
  A.   4x + 7y = 6 → 4x + 7y = 6
(6x + y = 2)(-7)→ -42x - 7y = -14
  B.4x + 7y = 6x + y
  C.y = -6x + 2 → 4x + 7(-6x + 2) = 6
  D.(4x + 7y) + (6x + y) = 8
  E.(4x + 7y) - (6x + y) = 4

27. Solve the system of equations.
3x - 4y = -10 and 5x + 8y = -2
  A.(1, 2)
  B.(2, 1)
  C.(1, -2)
  D.(-2, 1)


28. The sum of two numbers is 51. Their difference is 13. What is the smaller of the two numbers?
  A.18
  B.19
  C.20
  D.21


29. Choose the correct first step(s) to solve the system using substitution.
y = 5x and 2x + 3y = 34
  A.(- 5x + y = 0)(-3)→ 15x - 3y = 0
2x + 3y = 34 → 2x + 3y = 34
  B.2x + 3(5x) = 34
  C.5x = 2x + 3y
  D.5x + (2x + 3y) = 34
  E.5x - (2x - 3y) = -34

30. Solve the system of equations.
6x + 2y = 10 and -6x - 2y = 12
  A.(0, 5)
  B.(-1, 8)
  C.(2, -1)
  D.no solution
  E.infinitely many solutions


31. Solve the system of equations.
4x + 7y = 6 and 6x + 5y = 20
  A.(5, 2)
  B.(-5, 2)
  C.(5, -2)
  D.no solution
  E.infinitely many solutions

Answer
1. A, 2. B, 3. B, 4. B, 5. A, 6. A
7. 9x+12y=-6, 8x12y=40, add equations to get x=2, y=-2
8. C, 9. D, 10. C
11. add equations to get 2x=10, x=5, y=2
12. D
13. 2x+y=46, y=x+4, x=14, y=18
14. m+5f=25, m+10f=40, m=10, f=3
15. x+y=170, x-y=26, x=98, y=72
16-21 repeats
22. x+y=100, 0.24x+0.50y = 100(0.36), x=53.85, y=46.15
24. A, 25. D, 26. A, 27. D, 28. B, 29. B, 30. D, 31. C