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shelby1290

  • one year ago

Solve by elimination. Check each solution. a) 38 = 2x - 5y 75 = 7x - 3y b) 6x + 5y = 22 3y= 4x + 36

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  1. theopenstudyowl
    • one year ago
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    make one of the terms have the same number in both equations and then subtract.....

  2. shelby1290
    • one year ago
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    @theopenstudyowl how do you do that?

  3. UsukiDoll
    • one year ago
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    shall we start on this problem first? a) 38 = 2x - 5y 75 = 7x - 3y

  4. UsukiDoll
    • one year ago
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    so... let's eliminate the x first we do this through multiplication.. the first equation must be negative because when we add numbers... for example if I have -7x +7x the x cancels out... so looking at the x term only we have 2x and 7x.

  5. UsukiDoll
    • one year ago
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    I need to multiply the first equation by -7 and multiply the second equation by 2 because our goal is to create the same number and if we're going to add..at least one of the numbers must be negative to get rid of our x.

  6. UsukiDoll
    • one year ago
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    \[-7(38=2x-5y)\] \[2( 75 = 7x - 3y )\]

  7. UsukiDoll
    • one year ago
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    welcome back :)

  8. shelby1290
    • one year ago
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    sure

  9. UsukiDoll
    • one year ago
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    so can you distribute the -7 in the first equation and the 2 in the second equation ?

  10. shelby1290
    • one year ago
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    lol sorry i was having wifi problems

  11. UsukiDoll
    • one year ago
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    oh that's ok... my isp provider is bad too :P

  12. shelby1290
    • one year ago
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    |dw:1434511952976:dw|

  13. shelby1290
    • one year ago
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    |dw:1434512046087:dw|

  14. shelby1290
    • one year ago
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    are those correct?

  15. UsukiDoll
    • one year ago
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    I can check the second one without pen and paper... I need a calculator for the first xD

  16. UsukiDoll
    • one year ago
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    yeah they are.

  17. UsukiDoll
    • one year ago
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    \[-266=-14x+35y\] \[150=14x-6y\]

  18. UsukiDoll
    • one year ago
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    now we can add these two equations together.

  19. UsukiDoll
    • one year ago
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    you will notice that the x's disappear and that's what we want.

  20. UsukiDoll
    • one year ago
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    so what is -266+

  21. UsukiDoll
    • one year ago
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    OH My bad what is -266+150 and 35y-6y

  22. shelby1290
    • one year ago
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    -266 + 150 = -116

  23. shelby1290
    • one year ago
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    35y-6y=29y

  24. UsukiDoll
    • one year ago
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    we need to use addition because we want the -14x+14x to cancel out. yes that's correct -266+150=-116 and yes 35y-6y=29y

  25. shelby1290
    • one year ago
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    what must we add?

  26. UsukiDoll
    • one year ago
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    we need to use addition so that the -14x and the 14x cancel out... we need to use addition for the first and second equation... you're doing good so far :)

  27. UsukiDoll
    • one year ago
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    -116=29y now we just need division

  28. shelby1290
    • one year ago
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    |dw:1434512501123:dw|

  29. UsukiDoll
    • one year ago
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    very good! :) luckily that was the hard part of doing this problem... once we have one of our variables we can just solve for x We can choose to substitute y=-4 in one of these equations 38 = 2x - 5y 75 = 7x - 3y I think using the first equation will be easier 38 = 2x - 5(-4)

  30. shelby1290
    • one year ago
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    |dw:1434512671123:dw|

  31. shelby1290
    • one year ago
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    lol i really don't know what i just did there ^

  32. UsukiDoll
    • one year ago
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    that's good :) if you have x = 9 and y = -4 plug it back into those two equations... if you have 38=38 it's correct... and you have the right x and y values.

  33. UsukiDoll
    • one year ago
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    38 = 2x - 5y 75 = 7x - 3y try plugging in x = 9 and y = -4 to see if 38=38 and 75=75

  34. UsukiDoll
    • one year ago
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    then you know that your x and y values are correct.

  35. UsukiDoll
    • one year ago
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    38 = 2(9) - 5(-4) 38=18+20 38=38 75 = 7(9) - 3(-4) 75= 63+12 75=75 so our answer is correct :) x = 9 and y = -4

  36. shelby1290
    • one year ago
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    so x=9 and y=-4 are our final answers?

  37. shelby1290
    • one year ago
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    @UsukiDoll do i have to follow the same steps for part b?

  38. UsukiDoll
    • one year ago
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    yes

  39. UsukiDoll
    • one year ago
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    but you need to rearrange the second equation... b) 6x + 5y = 22 3y= 4x + 36

  40. UsukiDoll
    • one year ago
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    you just have to subtract 4x on both sides and switch places I'll do that part for you 3y-4x=4x-4x+36 3y-4x=36 -4x+3y=36 so now you have 6x+5y=22 -4x+3y=36

  41. UsukiDoll
    • one year ago
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    we could get rid of the x again see we already have a negative sign on the second equation .. so we multiply the 4 throughout the first equation and 6 throughout the second equation 4(6x+5y=22) 6(-4x+3y=36)

  42. shelby1290
    • one year ago
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    okay and then distribute?

  43. UsukiDoll
    • one year ago
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    yes :)

  44. shelby1290
    • one year ago
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    |dw:1434515008507:dw|

  45. shelby1290
    • one year ago
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    |dw:1434515088427:dw|

  46. UsukiDoll
    • one year ago
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    24x+20y=88 -24x+18y=216 yes.. now we use addition to get rid of the x

  47. shelby1290
    • one year ago
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    do i add all of them or just 24x + (-24x)

  48. UsukiDoll
    • one year ago
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    you add all of them

  49. shelby1290
    • one year ago
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    |dw:1434515403562:dw|

  50. UsukiDoll
    • one year ago
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    yes the x cancels out.. you don't have to write 0 ... just 38y=304 and then we use division to have y = ?

  51. shelby1290
    • one year ago
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    y=8

  52. UsukiDoll
    • one year ago
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    alright... since we have y=8, we can choose to place y=8 in the first or second equation... 6x+5y=22 -4x+3y=36

  53. shelby1290
    • one year ago
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    is it easier to substitute into the 1st of 2nd equation? i was going to go with the 2nd but im not sure

  54. shelby1290
    • one year ago
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    or 2nd*

  55. UsukiDoll
    • one year ago
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    substitution method works too, but your question is asking elimination method, so we're forced to do it that way.

  56. shelby1290
    • one year ago
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    i'm not very good at elimination lol

  57. shelby1290
    • one year ago
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    and i have my final exam tmrrw oh boyyyyy

  58. UsukiDoll
    • one year ago
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    elimination method for these equations means that we either need the x to cancel or the y to cancel... so we need to use multiplication and figure out what number do I need to multiply to have at least one of the x's and y's to be the same. we need to have at least one positive number and one negative number so when we add the x or the y should cancel.

  59. shelby1290
    • one year ago
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    okay

  60. UsukiDoll
    • one year ago
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    so getting back to 6x+5y=22 -4x+3y=36 since we have y = 8 we can choose one of these equations and solve for x

  61. shelby1290
    • one year ago
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    ok i'll go with the 2nd one

  62. UsukiDoll
    • one year ago
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    -4x+3(8)=36

  63. UsukiDoll
    • one year ago
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    what is 3 x 8 ?

  64. shelby1290
    • one year ago
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    24

  65. UsukiDoll
    • one year ago
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    -4x+24=36 so we subtract 24 on both sides

  66. shelby1290
    • one year ago
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    |dw:1434516225078:dw|

  67. shelby1290
    • one year ago
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    idk why but i got confused

  68. UsukiDoll
    • one year ago
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    well we need to shift the 24 to the right, so to do that I need to subtract because I want to get rid of the 24 on the left

  69. UsukiDoll
    • one year ago
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    -4x+24-24=36-24

  70. UsukiDoll
    • one year ago
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    24-24 is 0 so the 24 is no longer on the left side... but I do have 24 on the right side which is what I need -4x=36-24

  71. shelby1290
    • one year ago
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    |dw:1434516414467:dw|

  72. UsukiDoll
    • one year ago
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    alright so now we have x = -3 and y = 8

  73. UsukiDoll
    • one year ago
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    now we can check 6x+5y=22 -4x+3y=36 x=-3 and y=8 must satisfy both of these equations

  74. shelby1290
    • one year ago
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    |dw:1434516608979:dw|

  75. UsukiDoll
    • one year ago
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    the second one seems easier to check -4(-3)+3(8) = 36 12+24=36 36=36 6(-3)+5(8)=22 -18+40=22 22=22 yay!

  76. shelby1290
    • one year ago
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    @UsukiDoll thanks for all of the help and remaining patient with me. I'm so nervous for my final exam tomorrow. I'm not the best at math at all!

  77. UsukiDoll
    • one year ago
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    :)...mathematics is always cumulative and requires a ton of practice.

  78. shelby1290
    • one year ago
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    yes i know and now the jokes on me for not doing my homework each night lol

  79. UsukiDoll
    • one year ago
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    just try your best :)

  80. shelby1290
    • one year ago
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    thanks:)

  81. UsukiDoll
    • one year ago
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    does your teacher use curved grading?

  82. shelby1290
    • one year ago
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    what's curved grading?

  83. UsukiDoll
    • one year ago
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    instead of grading A B C D F.. curved grading is used to give more students who think they are going to fail , better grades... so a 80-100 will end up being an A instead of 90-100 being an A on regular grading.

  84. UsukiDoll
    • one year ago
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    http://academics.hamilton.edu/biology/smiller/curve.html

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