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simultaneous equation i need help with Watch

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    x+2y=3
    x^2-2y+4y^2=18

    the textbook says the answers are x =1.5, y=2.25; x=4, y =-0.5 but i've tried all ways I know used up 4 pages and haven't gotten any of the right answers so any help would be greatly appreciated
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    (Original post by Jsv1997)
    x+2y=3
    x^2-2y+4y^2=18

    the textbook says the answers are x =1.5, y=2.25; x=4, y =-0.5 but i've tried all ways I know used up 4 pages and haven't gotten any of the right answers so any help would be greatly appreciated
    Rearrange equation 1 to find x in terms of y.

    Substitute x in terms of y into equation 2, then solve the quadratic for y.

    Substitute the values of y into equation 1 to find x.

    Done.
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    Might sound really advanced lol or long but here it is:
    Substitute x from the first equation Into the second by rearranging the equation.

    X = y - 2x
    Substitute x into the second equation.
    Let's see how you do from there, if you need further help, just reply back and I'm ready to help.
    There are 2 ways to get to both of hype answers and I've got both of them but I can't give the full answer 😀 so this is a starter.


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    could try altering the lnear equation to read:

    x=(3-2y) sub this into the equation for the ellipse, and simplify (expand).

    You should get:

    8y^{2}-14y-9=0 which can be factorised...
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    (Original post by Jsv1997)
    x+2y=3
    x^2-2y+4y^2=18

    the textbook says the answers are x =1.5, y=2.25; x=4, y =-0.5 but i've tried all ways I know used up 4 pages and haven't gotten any of the right answers so any help would be greatly appreciated
    You can write the second equation as (x+2y)^2 - 2y(2x+1)=18. And then you know x+2y=3 and you can also rearrange this to get 2y=3-x and substitute that in.
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    (Original post by Hasufel)
    could try altering the lnear equation to read:

    x=(3-2y) sub this into the equation for the ellipse, and simplify (expand).

    You should get:

    8y^{2}-14y-9=0 which can be factorised...
    That is too much lol, the answer is obvious now. But meh... I was gonna do that too


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    (Original post by Jsv1997)
    x+2y=3
    x^2-2y+4y^2=18

    the textbook says the answers are x =1.5, y=2.25; x=4, y =-0.5 but i've tried all ways I know used up 4 pages and haven't gotten any of the right answers so any help would be greatly appreciated
    thanks for all the help I checked it over it turns out I had the numbers wrong after factorizing I had (4x+1)(2x-9) instead of (4x-9)(2x-1) but thanks for all the help anyway
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    (Original post by Jsv1997)
    thanks for all the help I checked it over it turns out I had the numbers wrong after factorizing I had (4x+1)(2x-9) instead of (4x-9)(2x-1) but thanks for all the help anyway
    Now that you understood how to get the answer, I'll show you the other way I was talking about, a bit weird lol but yeh.

    First of all, substitute the 1st linear equation into the next equation.

    x = 2y - 3
    Therefore, x^2 - 2y + 4y^2 = 18 becomes (3-2y)^2 - 2y + 4y^2 = 18.

    This is now 9-6y-6y+4y^2-2y+4y^2 = 18
    Simplify it > 9 - 12y + 4y^2 - 2y + 4y^2 = 18
    Then, 8y^2 - 14y + 9 = 18
    8y^2 - 14y = 9
    Factorise it, 2y(4y - 7) = 9
    Therefore, 2y(4y) = 2
    8y^2 = 2
    Divide both sides by 8 to get y^2.
    y^2 = 2/8 = 0.25 or 1/4
    Square root both sides
    y = square root of 0.25 = 0.5

    I don't know how to get to -0.5 though lel. Maybe it's this:

    2y(4y - 7) = 9
    Therefore, 2y(4y) = 9 + 7 = 16
    8y^2 = 16
    Square root both sides, 8y = -4 or 4, i choose -4.
    -4 / 8 = -0.5

    Or you can use the quadratic formula and get the answers, much faster and easier .
 
 
 
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