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anonymous

  • 5 years ago

some one plz help me need help solve the system of equations by graphing then classify the system as consistent or inconsistent, and as dependent or independent 4x-y=15 x+5y=-12 step by step plz

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  1. anonymous
    • 5 years ago
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    These are linear equations in two variables If they have a common solution, then they will cross each other at a point and hence will be consistent. We put them in the form ax + by + c = 0 4x - y - 15 = 0 and x + 5y + 12 = 0 Now If a1/a2≠b1/b2 then they will intersect at one point and will have a unique and consistent solution Here a1/a2 = 4/1 and b1/b2 = -1/5 Since a1/a2 is not equal to b1/b2, therefore it will have a unique solution and they are consistent.

  2. anonymous
    • 5 years ago
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    Also since they share only one common point, they are consistent and independent

  3. anonymous
    • 5 years ago
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    For your info, if \[a1/a2 \neq b1/b2\] then they are consistent and independent as they will cut each other at one point if \[a1/a2 = b1/b2 = c1/c2\] then they r consistent a dependent as the two lines will lie on each other if \[a1/a2 = b1/b2 \neq c1/c2\] then they r independent as they r parallel lines and will not meet/cut each other at even one point Hope this clears everything....

  4. anonymous
    • 5 years ago
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    tina ????

  5. anonymous
    • 5 years ago
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    im more confused

  6. anonymous
    • 5 years ago
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    Why??

  7. anonymous
    • 5 years ago
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    because i have no idea how to do this

  8. anonymous
    • 5 years ago
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    the other guy is telling me one thing and someone else told me another

  9. anonymous
    • 5 years ago
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    First you have to put the given equations in ax + by + c = 0 form See how I did it.... Is that clear or not??

  10. anonymous
    • 5 years ago
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    yes

  11. anonymous
    • 5 years ago
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    ok so 4x-y+15=0?

  12. anonymous
    • 5 years ago
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    No it will be - 15 becoz when you shift a term from one side to the other, its sign changes

  13. anonymous
    • 5 years ago
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    So, it will be 4x -y - 15 = 0

  14. anonymous
    • 5 years ago
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    ok and x+5y-12=0 for the second equation?

  15. anonymous
    • 5 years ago
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    No, x + 5y + 12 = 0 as sign on - 12 will become + when it is shifted to the other side.

  16. anonymous
    • 5 years ago
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    ok then what

  17. anonymous
    • 5 years ago
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    Now we check what is the ratio of the coefficients of x in the two equations. Here a1/a2 = 4/1 as in first eqn it is 4x and in the second eqn it is 1

  18. anonymous
    • 5 years ago
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    Then we check for the ratio of the coefficients of the y in the two equations Here b1/b2 = -1/5 as in first eqn it is -y and in second eqn it is 5y

  19. anonymous
    • 5 years ago
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    Finally we check for the ratio of the constant terms in the two equations here c1/c2 = -15/12

  20. anonymous
    • 5 years ago
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    Clear till now??

  21. anonymous
    • 5 years ago
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    nope lost me when you started talking about ratio's 5y

  22. anonymous
    • 5 years ago
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    U u/sttod a1/a2 = 4/1 ??

  23. anonymous
    • 5 years ago
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    yes it is 4x

  24. anonymous
    • 5 years ago
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    I guess it wud be easier if cud talk, do u hv a SKYPE account???

  25. anonymous
    • 5 years ago
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    I hv a SKYPE id hakki.singh

  26. anonymous
    • 5 years ago
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    not anymore

  27. anonymous
    • 5 years ago
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    well it wud hv been very easy if we cud talk.....

  28. anonymous
    • 5 years ago
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    i dont remember any of this from the hmwk

  29. anonymous
    • 5 years ago
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    Maybe u are being taught a different method, mine is very simple and easy to follow if u get the hang once

  30. anonymous
    • 5 years ago
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    x=0 then y=

  31. anonymous
    • 5 years ago
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    No, first u hv to look at the coefficients of the x terms of both equns In the first one 4 is the coefficient of the term 4x In the second one 1 is the coefficient of the term x

  32. anonymous
    • 5 years ago
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    Clear??

  33. anonymous
    • 5 years ago
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    ok

  34. anonymous
    • 5 years ago
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    So, a1/a2 ie the ratio of the coefficients of the x terms of the first eqn and the second eqn is 4/1

  35. anonymous
    • 5 years ago
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    clear??

  36. anonymous
    • 5 years ago
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    ok

  37. anonymous
    • 5 years ago
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    Now we go the y terms

  38. anonymous
    • 5 years ago
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    In the first eqn it is -y and in the second eqn it is 5y so b1 is -1 abd b2 is 5 so b1/b2 is -1/5

  39. anonymous
    • 5 years ago
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    clear??

  40. anonymous
    • 5 years ago
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    ok

  41. anonymous
    • 5 years ago
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    Finally we look at the constant terms Here it is -15 in the first eqn and 12 in the second eqn So, c1/c2 is -15/12

  42. anonymous
    • 5 years ago
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    Clear??

  43. anonymous
    • 5 years ago
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    ok

  44. anonymous
    • 5 years ago
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    Now we have to understand the terms consistent/inconsistent and dependent/independent

  45. anonymous
    • 5 years ago
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    consistent means that the two eqns share at least one or more solutions This means that if their graphs cut each other at one point or the two lines coincide in which case they share infinite solutions inconsistent means that they do not share even one solution i.e. the line never meet

  46. anonymous
    • 5 years ago
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    Got it??

  47. anonymous
    • 5 years ago
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    yes

  48. anonymous
    • 5 years ago
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    And in case they r consistent i.e they share one or more solutions, then they will be independent if they share just one solution and dependent if they share many solutions ie.e the line coincide

  49. anonymous
    • 5 years ago
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    So we can have consistent and dependent consistent and independent and inconsistent

  50. anonymous
    • 5 years ago
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    Clear??

  51. anonymous
    • 5 years ago
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    it is only one answer and the solution of the system typed in an ordered pair,

  52. anonymous
    • 5 years ago
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    I'm coming to the solution, but is the above classifications as consistent and dependent, consistent and independent and inconsistent clear??

  53. anonymous
    • 5 years ago
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    yes

  54. anonymous
    • 5 years ago
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    Fianlly, if a1/a2≠b1/b2 then they are consistent and independent as they will cut each other at one point if a1/a2=b1/b2=c1/c2 then they r consistent a dependent as the two lines will lie on each other if a1/a2=b1/b2≠c1/c2 then they r inconsistent as they r parallel lines and will not meet/cut each other at even one point

  55. anonymous
    • 5 years ago
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    In your case a1/a2 = 4/1 and b1/b2 = -1/5 So, a1/a2 is not equal to b1/b2, so your pair of equations is consistent and independent

  56. anonymous
    • 5 years ago
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    Clear??

  57. anonymous
    • 5 years ago
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    yes

  58. anonymous
    • 5 years ago
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    So, it is now clear tht yr system of pair of eqns is consistent and independent. To draw their graphs, you modify the first equation by separating x and y as follows 4x - 15 = y Now put various values like -1 , 0, 1, 4 for x and getting corresponding values of y Understood??

  59. anonymous
    • 5 years ago
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    yes

  60. anonymous
    • 5 years ago
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    Similarly modify the second eqn as follows: 5y = -x -12 (remember signs change when you shift their side) so, -x -12 y = ----------- 5 Now, put various values for x and calculate corresponding values of y. Now plot the graphs for the two eqns separately and you will find them cutting each other at one point.

  61. anonymous
    • 5 years ago
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    Clear????

  62. anonymous
    • 5 years ago
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    Your intersection point shud b (3, -3)

  63. anonymous
    • 5 years ago
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    Hope now everything is clear??

  64. anonymous
    • 5 years ago
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    ok and it is consistent and independent

  65. anonymous
    • 5 years ago
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    yes it is

  66. anonymous
    • 5 years ago
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    ok ty so much for all your help I really appreciate it

  67. anonymous
    • 5 years ago
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    U r welcome. In this we have to be clear what consistent/inconsistent and dependent/independent mean. Then using the three ratio checks we can find whether there will be one solution, many solutions or no solution. Do I get a medal for this??

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