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lovelycharm

  • one year ago

What are the x-coordinates of the solutions to this system of equations? x2 + y2 = 16 y = x + 4

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  1. Vocaloid
    • one year ago
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    do a substitution y = x + 4 means we can replace "y" with "x + 4" when we see y, so x^2 + y^2 = 16 x^2 + (x+4)^2 = 16 know where to go from here?

  2. lovelycharm
    • one year ago
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    then u divide the by 4

  3. Vocaloid
    • one year ago
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    uhhhh not quite

  4. Vocaloid
    • one year ago
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    then we can use FOIL to expand (x+4)^2

  5. lovelycharm
    • one year ago
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    2x+8

  6. Vocaloid
    • one year ago
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    not quite, the ^2 is an exponent (x+4)^2 = (x+4)(x+4) = ?

  7. lovelycharm
    • one year ago
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    0

  8. Vocaloid
    • one year ago
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    nope, not quite... hint: (x+A)(x+A) = x^2 + 2*A*x + A^2 (x+4)(x+4) = ____________________ fill in the blank

  9. lovelycharm
    • one year ago
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    x+4x+4x+16

  10. Vocaloid
    • one year ago
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    almost, you're very close! x^2 + 4x + 4x + 16

  11. Vocaloid
    • one year ago
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    that simplifies to: x^2 + 8x + 16, with me so far?

  12. lovelycharm
    • one year ago
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    2x+8x+16 4x+16

  13. Vocaloid
    • one year ago
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    nope, not quite. please remember that x^2 is NOT equal to 2x

  14. Vocaloid
    • one year ago
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    x^2 means x*x, ok?

  15. lovelycharm
    • one year ago
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    so it was x+8x+16

  16. lovelycharm
    • one year ago
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    confuse

  17. Vocaloid
    • one year ago
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    yes, x^2 + 8x + 16, with me so far?

  18. lovelycharm
    • one year ago
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    x+4^2

  19. Vocaloid
    • one year ago
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    no, we just leave it as x^2 + 8x + 16, ok?

  20. lovelycharm
    • one year ago
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    What are the x-coordinates of the solutions to this system of equations? x2 + y2 = 16 y = x + 4 −4 and 0 4 and 0 −2 and −3 2 and −3

  21. lovelycharm
    • one year ago
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    those r the option

  22. Vocaloid
    • one year ago
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    right, we'll get to that in a minute, ok?

  23. Vocaloid
    • one year ago
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    right now we have: (x+4)^2 = x^2 + 8x + 16 plugging that back into the first equation gives us x^2 + x^2 + 8x + 16 = 16 know where to go from here?

  24. lovelycharm
    • one year ago
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    no not really

  25. Vocaloid
    • one year ago
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    start by subtracting 16 from each side.

  26. lovelycharm
    • one year ago
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    0

  27. Vocaloid
    • one year ago
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    what about the left side? x^2 + x^2 + 8x + 16 - 16 = ?

  28. lovelycharm
    • one year ago
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    4

  29. Vocaloid
    • one year ago
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    nope, maybe this will make things easier: (x^2 + x^2 + 8x) + 16 - 16 = ?

  30. lovelycharm
    • one year ago
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    8x^2+0

  31. lovelycharm
    • one year ago
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    2x^2+8x

  32. Vocaloid
    • one year ago
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    good, 2x^2 + 8x

  33. Vocaloid
    • one year ago
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    now we have 2x^2 + 8x = 0 solve for x

  34. lovelycharm
    • one year ago
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    4x+8x=0 4x=0

  35. Vocaloid
    • one year ago
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    remember what I said earlier? x^2 is NOT 2x

  36. Vocaloid
    • one year ago
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    2x^2 + 8x = 0 2x(x+4) = 0 solve for x

  37. lovelycharm
    • one year ago
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    2x2+8x

  38. Vocaloid
    • one year ago
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    not quite... 2x^2 + 8x is what I gave you to start with

  39. Vocaloid
    • one year ago
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    2x = 0 x = ?

  40. lovelycharm
    • one year ago
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    4

  41. Vocaloid
    • one year ago
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    try again

  42. Vocaloid
    • one year ago
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    2x = 0 divide both sides by 2

  43. lovelycharm
    • one year ago
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    0

  44. Vocaloid
    • one year ago
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    good

  45. Vocaloid
    • one year ago
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    now we solve (x+4) = 0 x = ?

  46. lovelycharm
    • one year ago
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    4

  47. Vocaloid
    • one year ago
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    almost but not quite

  48. Vocaloid
    • one year ago
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    subtract 4 from each side

  49. lovelycharm
    • one year ago
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    -4

  50. Vocaloid
    • one year ago
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    good, so our solutions are 0 and -4

  51. lovelycharm
    • one year ago
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    thank u so much

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