# Project #38972 - ALGEBRA

Please if you can do this assignement in Microsoft WORD.

Find the solution of ordered pairs for the following systems. Show all your work:

1. y = -1/2x – 2 and 2x – y = 4

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2. 3x – y = 2 and –y = 4x + 2 =

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3. 1/3x – y = 1 and 1/4x – y = 1

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Solve each system by graphing. Determine if the system is consistent or

inconsistent.

4. 2x + 3y = 3 and 4x + 6y = -12

5. 3x -2y = -1 and 2x – 4y =

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6. y = -1 and x = -2

7. x –y = 1 and y = 2

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8. 3x + 3y = 21 and 3x + 4y = 24

9. 3x + 2y = 5 and 9x + 6y = 12

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10. 2x + y = -6 and x = -3

Use the substitution method to solve for the system of equations. If the solution is

dependent or inconsistent, then identify them as such.

11. .25x + 75y = 4 and x – y = 4

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12. .5x + .5y = 5 and y = x + 2.5

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17. 3x + 2y = -3 and 2x + 3y = -2

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18. 3x + 4y = 0 and x + 4y = -2

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19. 1/3 x + ½ y = 6 and 2x – y = 4

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Solve the system for each variable, and check your solutions. Show all your work:

20. x + 3y and z = 4x and x + y + z = 8

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20. x + y + z = 60 and x – z = y + 6 and y = 40 – x – 3z

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22. 2x + y + 4z = 3 and x + 2y = 2z -3 and 4z + 3y = 0

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23. x + y + z = 1 and 2x – y + 3z = 4.5 and 4x -5y – 5z = -0.5

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Now, write a system of two equations for each problem and then solve. Show all

21. A metal alloy that is made up of 15% aluminum is combined with a metal alloy that

is 35% aluminum. If the result is 400 Kilograms of 27.5% of aluminum alloy, then

how much of each alloy was used?

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Now, write a system with three equations for each of the problems and solve. Show all your work.

25. If the digits of a three-digit number are reversed in order, then the sum of the new

resulting number and the original number comes out to be 665. The difference of the two numbers is 297. The tens’ digit place is two times the hundreds’ place digit. What is the number?

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26. How many different ways can you make combinations of 3 letters out of the five-letter word LEARN?

27. How many different ways can you make combinations of 2 numbers out of the five

different single digit numbers?

28. How many different ways can you make combinations of 6 numbers out of the

numbers 0 through 9?

29. How many different ways can you make combinations of 3 letters out of the five-letter word COMBINE?

30 . How many different ways can you make combinations of 5 letters out of the five-letter word COMBINED?

31. How many diagonals can be drawn from each vertex of a pentagon?

32. How many diagonals can be drawn from each vertex of a decagon?

33. How many diagonals can be drawn from each vertex of a dodecagon (12-sided

shape)?

using the combination formula and probability formulas.

34. A classroom is made up of 11 boys and 14 girls. The teacher has four main classroom responsibilities that she wants to hand out to four different students (one for each of the four students). If the teacher chooses 4 of the students at random, then what is the probability that the four students chosen to complete the responsibilities will be all boys?

35. A woman has 14 different shirts: 10 white shirts and 4 red shirts. If she randomly

chooses 2 shirts to take with her on vacation, then what is the probability that she will

choose two white shirts? Show your answer in fraction and percent, round to the

nearest whole percent.

36. A student has written the numbers 0 through 9 each separately on 10 different index

cards. If 3 cards were drawn at random, then what is the probability that the sum of all

the 3 numbers on the cards would be equal to 12?

If a card is pulled from a deck of playing cards and a six-sided die is tossed, then

what is the probability that the following two independent events will occur:

37. Rolling an 8 and drawing an even numbered card.

38. Rolling a factor of 6 and drawing a red King.

(Draw a pie circular spinner with 5 sides in each side label A-E) If a dice is rolled and the spinner with 5 sides, each with the letters A, B, C, D, E is spun, then what is the probability of the following independent events occurring at the same time?

39. Spinning B and an even number.

40. Spinning a vowel and not rolling an even number.

(Draw a pie circular spinner with 3 sides in each side label X-Z) Identical dials are spun, each dial contains X, Y, and Z. What is the probability that:

41. 6 identical spinners would not land on Z? Round your answer to the nearest whole

percent.

42. 8 identical spinners would not land on Y? Round your answer to the nearest whole

percent.

A dealer holds a shuffled deck of 52 playing cards and draws cards at random.

Determine the probably that the following events would occur, without replacement.

43. The first card dealt is the king of clubs and the second card dealt is the queen of clubs.

44. The first three cards are hearts.

45. 6 different numbers are drawn on separately on 11 different cards, one number on

each card. There is one 1, three 2’s, two 3’s, three 4’s, one 5, and one 6. 3 cards are

drawn in a row with replacement. What is the probability that they are all 6’s?

 Subject Mathematics Due By (Pacific Time) 09/05/2014 12:00 pm
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