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anonymous

  • 5 years ago

Solve using the substitution method. 5x − 7y = −16, 2x + 8y = 26

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  1. Mertsj
    • 5 years ago
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    Divide the second equation by 2 and solve it for x You will get x=13-4y Put that into the first equation in place ofx

  2. anonymous
    • 5 years ago
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    i would use the 2nd equation to substitute because the numbers are more simple. get down to x =( ) so 2x +8y = 26 2x = 26 -8y x = (26 - 8y)/2 x = 13 -4y now you can replace this x into the other equation 5x - 7y = -16 replace the x 5(13 - 4y) - 7y = -16 65 - 20y - 7y = -16 solve for y -27y = -71 y = 3 replace y=3 into any equation to find x 2x + 8y = 26 2x + 8(3) = 26 2x + 24 = 26 2x = 2 x =1 y = 3

  3. anonymous
    • 5 years ago
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    Ok mertsj I am still confused

  4. Mertsj
    • 5 years ago
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    Can you divide the second equation by 2?

  5. Mertsj
    • 5 years ago
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    |dw:1327112923657:dw|

  6. anonymous
    • 5 years ago
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    Ok I got that part

  7. Mertsj
    • 5 years ago
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    Now subtract 4y from both sides.

  8. anonymous
    • 5 years ago
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    so 4y-y7 and 13-4y

  9. Mertsj
    • 5 years ago
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    |dw:1327113113852:dw|

  10. Mertsj
    • 5 years ago
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    So do you know how to substitute that in the other equation?

  11. anonymous
    • 5 years ago
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    somewhat

  12. Mertsj
    • 5 years ago
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    Do you play a sport?

  13. Mertsj
    • 5 years ago
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    A team sport?

  14. anonymous
    • 5 years ago
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    no

  15. Mertsj
    • 5 years ago
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    Do you watch sports on tv?

  16. anonymous
    • 5 years ago
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    no sorry

  17. Mertsj
    • 5 years ago
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    Well I thought you might know what it means when the coach substitutes one player for another. Any way, we have to take that name for x that we just found and replace x with it.

  18. anonymous
    • 5 years ago
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    would you divide the other side by 2 as weel

  19. anonymous
    • 5 years ago
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    well*

  20. Mertsj
    • 5 years ago
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    |dw:1327113311498:dw|

  21. Mertsj
    • 5 years ago
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    Do you understand what I just did?

  22. anonymous
    • 5 years ago
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    somewhat

  23. Mertsj
    • 5 years ago
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    Now use the distributive property and collect like terms

  24. anonymous
    • 5 years ago
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    now math is my worst subject how do you do that

  25. Mertsj
    • 5 years ago
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    5(13-4y)=65-20y

  26. Mertsj
    • 5 years ago
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    Do you get that?

  27. anonymous
    • 5 years ago
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    now how did you get that

  28. Mertsj
    • 5 years ago
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    The 5 outside the parentheses means to multiply everything in the parentheses by 5.

  29. anonymous
    • 5 years ago
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    ok

  30. Mertsj
    • 5 years ago
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    So I multiplied 5 by 13 and got 65. Then I multiplied -4y by 5 and got -20y

  31. Mertsj
    • 5 years ago
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    Now -20y and -7y are like terms and they should be combined.

  32. anonymous
    • 5 years ago
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    ok got that

  33. anonymous
    • 5 years ago
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    so would it be 27y

  34. Mertsj
    • 5 years ago
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    Now subtract 65 from both sides.

  35. Mertsj
    • 5 years ago
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    It's actually -27y

  36. Mertsj
    • 5 years ago
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    |dw:1327113544265:dw|

  37. anonymous
    • 5 years ago
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    ok got that part

  38. Mertsj
    • 5 years ago
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    Now divide both sides by -27

  39. anonymous
    • 5 years ago
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    so would it be -27y/-27y and -16/-27y

  40. Mertsj
    • 5 years ago
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    |dw:1327113866037:dw|

  41. Mertsj
    • 5 years ago
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    Did you subtract 65 from BOTH SIDES?

  42. anonymous
    • 5 years ago
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    yes I did than what do I do

  43. Mertsj
    • 5 years ago
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    So what do you have now? Then I can tell you what to do next.

  44. anonymous
    • 5 years ago
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    this is all I have down

  45. Mertsj
    • 5 years ago
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    Do you have -27y=-81 ?

  46. anonymous
    • 5 years ago
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    5x − 7y = −16 5(13-4y)-7y=-16 5(13-4y)=65-20y 65-20y-7y=-16 -20y+-7y=-27y 65-27y=-16 -65 -65 ----------- -27y/-27y=-81/-27 y=3 2x/2 + 8y/2 = 2b/2 x + 4y = 13 -4y -4y x=13-4y

  47. Mertsj
    • 5 years ago
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    So yes. y=3.

  48. Mertsj
    • 5 years ago
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    x=13-4y so replace y with 3 and find x

  49. Mertsj
    • 5 years ago
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    x=13-4(3) x=13-12 x=1

  50. anonymous
    • 5 years ago
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    ok and that how both of them end

  51. Mertsj
    • 5 years ago
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    -27y/-27y=-81/-27 That is a step you did. You should have divided by -27 and NOT by y just -27

  52. anonymous
    • 5 years ago
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    oh ok

  53. Mertsj
    • 5 years ago
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    So yes. The solution is x = 1 and y = 3 which is the ordered pair (1,3) And if you would graph those equations, the two lines would cross at the point (1,3)

  54. anonymous
    • 5 years ago
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    ok but its just says solve so I don't have to graph it right

  55. Mertsj
    • 5 years ago
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    That's right. You don't have to graph it. I just wanted you to know the connection between the solution of the system and the graph.

  56. anonymous
    • 5 years ago
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    oh ok great thank you so much you really helped

  57. Mertsj
    • 5 years ago
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    yw

  58. anonymous
    • 5 years ago
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    have a good night

  59. Mertsj
    • 5 years ago
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    You too.

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