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maths help please! (simultanious equation HL LC)

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  • 17-09-2014 11:09pm
    #1
    chocolate98
    Registered Users Posts: 192 ✭✭


    :confused:
    does anyone know how to work these out easily? :)
    2x-y=3
    3xy=15


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    #2
    Gryffindor
    Closed Accounts Posts: 133 ✭✭Gryffindor


    First, get find the equation either in terms of x or y. Y is easier in this case, as it is already on its own.

    2x-y=3
    -y=3-2x
    y=2x-3

    Then sub in

    3xy=15
    3x(2x-3)=15
    6x^2 - 9x =15

    Then just solve as a quadratic to find the x values.

    Sub these 2 x values back into the y equation to find the 2 y values


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    #3
    Gryffindor
    Closed Accounts Posts: 133 ✭✭Gryffindor


    First, find the equation either in terms of x or y. Y is easier in this case, as it is already on its own.

    2x-y=3
    -y=3-2x
    y=2x-3

    Then sub in

    3xy=15
    3x(2x-3)=15
    6x^2 - 9x =15

    Then just solve as a quadratic to find the x values.

    Sub these 2 x values back into the y equation to find the 2 y values


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    #4
    chocolate98
    Registered Users Posts: 192 ✭✭chocolate98


    Gryffindor wrote: »
    First, find the equation either in terms of x or y. Y is easier in this case, as it is already on its own.

    2x-y=3
    -y=3-2x
    y=2x-3

    Then sub in

    3xy=15
    3x(2x-3)=15
    6x^2 - 9x =15

    Then just solve as a quadratic to find the x values.

    Sub these 2 x values back into the y equation to find the 2 y values
    thank you sooo much my teacher goes way too quick :( thank you though :D


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    #5
    Bazzers
    Registered Users Posts: 65 ✭✭Bazzers


    Hi any one give me any help,need for tomoz these homework questions thanks!

    8a - 3b = 19
    9a + 5b =80


    4x. - 3y =30
    8x. + 5y =5


    6x - 7y = 3
    4x - 6y =-2


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    #6
    Bazzers
    Registered Users Posts: 65 ✭✭Bazzers


    so can ye help or not!


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    #7
    emersyn
    Registered Users Posts: 430 ✭✭emersyn


    Bazzers wrote: »
    !!!????

    Just apply the same method that Gryffindor used in the earlier post.
    An alternative method is to make either the value of the x or the value of the y from the first equation equal to that of the second equation but with an opposite sign, by multiplying both equations by appropriate numbers. Then add the equations - either the x or y will cancel giving you the value of the other unknown, then substitute the answer into one of the original equations to get the second unknown.
    Here's the first one done out.


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    #8
    blackbird 49
    Registered Users Posts: 411 ✭✭blackbird 49


    emersyn wrote: »
    Just apply the same method that Gryffindor used in the earlier post.
    An alternative method is to make either the value of the x or the value of the y from the first equation equal to that of the second equation but with an opposite sign, by multiplying both equations by appropriate numbers. Then add the equations - either the x or y will cancel giving you the value of the other unknown, then substitute the answer into one of the original equations to get the second unknown.
    Here's the first one done out.

    Got my son to do the first one, didn't show him your answer until finished got the same as you. Could you do the one from the original post he wants to see if he has it right, he's a leaving cert student, thanks


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    #9
    Bazzers
    Registered Users Posts: 65 ✭✭Bazzers


    Thanks also ill try and. Tackle the second, i can get so far but when i have to divide i always get a decimal point.


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    #10
    emersyn
    Registered Users Posts: 430 ✭✭emersyn


    blackbird 49 wrote: »
    Got my son to do the first one, didn't show him your answer until finished got the same as you. Could you do the one from the original post he wants to see if he has it right, he's a leaving cert student, thanks

    The one from the very first post? Seeing as one of the equations involves multiplication rather than just addition/subtraction, the way Gryffindor explained it is the only way to do it as far as I know. Use the formula for quadratics on the top of page 20 of the log tables (the quadratic is 6x^2 - 9x - 15=0 from Gryffindor's solution, so 'a' will be 6, 'b' will be -9 and 'c' will be -15) to get the two solutions for x and then put each solution into the original equation to get both values for y. I tried to do it out but I think my calculations went wrong somewhere as I got very long decimal figures :rolleyes:
    There should be some similar questions in your son's textbook that he can practice from and the solutions should be included in the back


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    #11
    Bazzers
    Registered Users Posts: 65 ✭✭Bazzers


    For d second q there 4x - 3y =30
    8x + 5y =5
    20x -15y = 150
    24x + 15y =15
    44x. =. 165
    44

    Where am i going wrong ?


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    #12
    Bazzers
    Registered Users Posts: 65 ✭✭Bazzers


    I multipled by x5 for top line and by x3 for second line


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    #13
    emersyn
    Registered Users Posts: 430 ✭✭emersyn


    Bazzers wrote: »
    For d second q there 4x - 3y =30
    8x + 5y =5
    20x -15y = 150
    24x + 15y =15
    44x. =. 165
    44

    Where am i going wrong ?

    You're on the right track, for the last step just divide the 165 by 44 to get x on its own and you'll get x = 3.75. Then put 3.75 back into one of the original equations in the place of x and you should get y = -5. All of your steps were correct


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    #14
    Bazzers
    Registered Users Posts: 65 ✭✭Bazzers


    9x + y =11)x8
    4x + 8y =20)
    72x + 8y = 88
    4x + 8y = 20

    76x. =. 118
    76 =x =1.5?


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    #15
    emersyn
    Registered Users Posts: 430 ✭✭emersyn


    Bazzers wrote: »
    9x + y =11)x8
    4x + 8y =20)
    72x + 8y = 88
    4x + 8y = 20

    76x. =. 118
    76 =x =1.5?

    The first equation needs to be multiplied by -8 instead of 8 as the y's need to cancel with the second equation:
    9x + y = 11 (-8)
    4x + 8y = 20
    ==> -72x -8y = -88
    4x + 8y = 20

    -68x = -68
    x = 1


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    #16
    Blue giant
    Registered Users Posts: 1,336 ✭✭✭Blue giant


    Bazzers wrote: »
    9x + y =11)x8
    4x + 8y =20)
    72x + 8y = 88
    4x + 8y = 20

    76x. =. 118
    76 =x =1.5?

    You need to multiply by the first equation by -8 to cancel the y as they then have opposite signs.

    -72x - 8y = -88
    4x + 8y = 20

    -68x = -68
    x = 68/68 = 1

    Edit: beaten to it by a second


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    #17
    Bazzers
    Registered Users Posts: 65 ✭✭Bazzers


    Thanks for your help much appreciated lads!!


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    #18
    blackbird 49
    Registered Users Posts: 411 ✭✭blackbird 49


    emersyn wrote: »
    The one from the very first post? Seeing as one of the equations involves multiplication rather than just addition/subtraction, the way Gryffindor explained it is the only way to do it as far as I know. Use the formula for quadratics on the top of page 20 of the log tables (the quadratic is 6x^2 - 9x - 15=0 from Gryffindor's solution, so 'a' will be 6, 'b' will be -9 and 'c' will be -15) to get the two solutions for x and then put each solution into the original equation to get both values for y. I tried to do it out but I think my calculations went wrong somewhere as I got very long decimal figures :rolleyes:
    There should be some similar questions in your son's textbook that he can practice from and the solutions should be included in the back

    Thanks for the reply he did the same as you and this is the answer he got,
    WHEN X=3 Y=3. WHEN X=1.5 Y=0


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    #19
    Bazzers
    Registered Users Posts: 65 ✭✭Bazzers


    Hi in class to day we were revising and got some homework questions? Any 1 help

    Inequalities
    X + 1<5,x€N


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    #20
    ko3p
    Registered Users Posts: 37 ✭ko3p


    Bazzers wrote: »
    Hi in class to day we were revising and got some homework questions? Any 1 help

    Inequalities
    X + 1<5,x€N

    Just treat the inequality sign as an equal to sign.
    From there, just take one from both sides and you get x < 4


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