Advertisement
If you have a new account but are having problems posting or verifying your account, please email us on hello@boards.ie for help. Thanks :)
Hello all! Please ensure that you are posting a new thread or question in the appropriate forum. The Feedback forum is overwhelmed with questions that are having to be moved elsewhere. If you need help to verify your account contact hello@boards.ie

maths help please! (simultanious equation HL LC)

  • 17-09-2014 11:09PM
    #1
    Registered Users, Registered Users 2 Posts: 192
    ✭✭


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


Welcome!

It looks like you're new here. Sign in or register to get started.

Comments

  • 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


  • 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


  • Registered Users, Registered Users 2 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


  • Registered Users, Registered Users 2 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


  • Registered Users, Registered Users 2 Posts: 65 Bazzers
    ✭✭


    so can ye help or not!


  • Advertisement
  • Registered Users, Registered Users 2 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.


  • Registered Users, Registered Users 2 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


  • Registered Users, Registered Users 2 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.


  • Registered Users, Registered Users 2 Posts: 430 emersyn
    ✭✭


    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


  • Registered Users, Registered Users 2 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 ?


  • Advertisement
  • Registered Users, Registered Users 2 Posts: 65 Bazzers
    ✭✭


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


  • Registered Users, Registered Users 2 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


  • Registered Users, Registered Users 2 Posts: 65 Bazzers
    ✭✭


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

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


  • Registered Users, Registered Users 2 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


  • Registered Users, Registered Users 2 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


  • Registered Users, Registered Users 2 Posts: 65 Bazzers
    ✭✭


    Thanks for your help much appreciated lads!!


  • Registered Users, Registered Users 2 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


  • Registered Users, Registered Users 2 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


  • Registered Users, Registered Users 2 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


Welcome!

It looks like you're new here. Sign in or register to get started.
Advertisement