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BeccaB003

  • one year ago

Solve the following system of equations. x^2 + y^2 = 9 x^2 - 3y = 9

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  1. BeccaB003
    • one year ago
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    These are the options: (-3, 0), (3, 0),(-3, 9),(3, 9) (-3, 9),(-3, 0) (-3, 0), (0, -3), (3, 0) (-3, 9) I am very confused on how to do this problem because there is a 3y and y^2

  2. anonymous
    • one year ago
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    well since they both = 9 its safe to say they equal each other right @BeccaB003

  3. anonymous
    • one year ago
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    hello

  4. anonymous
    • one year ago
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    well since they both = 9 its safe to say they equal each other right @BeccaB003

  5. BeccaB003
    • one year ago
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    I am here. Yes, I suppose they would equal each other.

  6. welshfella
    • one year ago
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    x^2 + y^2 = x^2 - 3y

  7. anonymous
    • one year ago
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    so x^2 + y^2 = x^2 - 3y now solve do -x^2 to get y^2+-3y

  8. anonymous
    • one year ago
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    i mean y^2=-3y

  9. welshfella
    • one year ago
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    subtract x^2 from both sides y^2 = - 3y

  10. BeccaB003
    • one year ago
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    @welshfella @DaBest21 But how do you solve with that problem if there is y and y^2?

  11. welshfella
    • one year ago
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    can you solve that?

  12. BeccaB003
    • one year ago
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    I thought you used substitution or elimination for problems like this.

  13. BeccaB003
    • one year ago
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    I don't understand how you would solve for y^2=3y ---they are two different types of variables. you can't combine them or anything.

  14. welshfella
    • one year ago
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    well i have used elimination - i eliminated x^2

  15. welshfella
    • one year ago
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    y^2 + 3y = 0 y(y + 3) = 0 y = ?

  16. welshfella
    • one year ago
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    you factor them as above

  17. BeccaB003
    • one year ago
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    y(y+3)=0 <---------- is factored

  18. BeccaB003
    • one year ago
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    I don't know how to simplify that more.

  19. welshfella
    • one year ago
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    when 2 functions are multiplied together and the result is 0 then either one or the other is zero. I other words there are 2 solutions y(y + 3) = 0 y = 0 or y + 3 = 0 y = 0 y= -3 0 and -3 are the 2 solutions

  20. BeccaB003
    • one year ago
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    So then you plug them both into the original equation to find x?

  21. welshfella
    • one year ago
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    yes plug them into x^2 - 3y = 9

  22. welshfella
    • one year ago
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    so when y = -3 x^2 -3(-3) = 9 x^2 + 9 = 9 x^2 = 9-9 = 0 x = 0 so one solution is (0,-3)

  23. BeccaB003
    • one year ago
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    Okay so, x^2 -3(0) = 9 equals: x^2 = 9 = x = 3

  24. BeccaB003
    • one year ago
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    So another solution is (3,0)

  25. welshfella
    • one year ago
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    not quite sqrt x^2 is also -3

  26. welshfella
    • one year ago
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    right (3,0) is one solution and a third one is (-3,0)

  27. welshfella
    • one year ago
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    * square root of 9 is also -3

  28. BeccaB003
    • one year ago
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    How can the square root of 9 be -3?

  29. welshfella
    • one year ago
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    so the 3rd option is the correct one.

  30. anonymous
    • one year ago
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    c

  31. welshfella
    • one year ago
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    3 * 3 = 9 also -3 * -3 = 9

  32. BeccaB003
    • one year ago
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    Okay, Thank you so much for your help! :)

  33. welshfella
    • one year ago
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    yw

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