Results 1 to 13 of 13

Math Help - Multiple Simultaneous Equations

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    79

    Multiple Simultaneous Equations

    How do I solve these by either substitution/ elimination? I'd also like to know how to solve them using matrices.

    U_n = an^{2}+bn+c=0
    U_1=4
    U_2=10
    U_3=18

    I need to find the values of the constants a, b, c are.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Quote Originally Posted by Viral View Post
    How do I solve these by either substitution/ elimination? I'd also like to know how to solve them using matrices.

    U_n = an^{2}+bn+c=0
    U_1=4
    U_2=10
    U_3=18

    I need to find the values of the constants a, b, c are.
    So it seems that U_n in general is the result of a,b and c combined with the value of n for each equation. How was U_1 formed? The same a,b and c were used, just a different n. You have 3 unknowns and potentially 4 equations so that's all you need.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    79
    Yeah I got that, and I sorted the U1, 2 and 3 into their respective equations. I've just never been shown how to solve simultaneous equations with more than 2 equations.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by Viral View Post
    How do I solve these by either substitution/ elimination? I'd also like to know how to solve them using matrices.

    U_n = an^{2}+bn+c=0
    U_1=4
    U_2=10
    U_3=18

    I need to find the values of the constants a, b, c are.
    Are
    U_1=4
    U_2=10
    U_3=18

    constant fubctions of x?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2009
    Posts
    79
    Not sure what you mean.

    U_1 = 16a + 4b + c =0
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Quote Originally Posted by Viral View Post
    Yeah I got that, and I sorted the U1, 2 and 3 into their respective equations. I've just never been shown how to solve simultaneous equations with more than 2 equations.
    Gotcha. Well you can use substitution here but it's tricky and a lot of algebra. If you want to use matrices like you said, first write out three equations. Make sure they are all in the same form, meaning the a's, b's and c's line up. Then make a 3x3 matrix of the left hand side of these three equations. Make another matrix that is 3x1 matrix of the right hand side of the three equations. If the first one is A and the second one is B, then take A^{-1}B and you'll get a 3x1 matrix as your answer which is the solution for a,b and c.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Sep 2009
    Posts
    79
    Hmm, actually we haven't learned how to work out the determinant of 3x3 matrices, only 2x2 matrices. How would I do this the algebraic way?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Quote Originally Posted by Viral View Post
    Hmm, actually we haven't learned how to work out the determinant of 3x3 matrices, only 2x2 matrices. How would I do this the algebraic way?
    Normally calculator's are allowed for this method.

    Anyway, if you want to do it by hand, it's just like with two variables. Solve an equation for one variable in terms of the others. You can do this a couple times and get two equations with two unknowns. Solve them normally then use that to find the 3rd solution.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Sep 2009
    Posts
    79
    Unfortunately calculators aren't allowed. I've tried doing what you've suggested and I've ended up with like a page of working out :S . I'll try again in the morning.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member
    Joined
    Sep 2009
    Posts
    79
    Ok, I've tried forever and I just can't work it out =\ . I somehow got c = 2 which I don't think is correct.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Viral View Post
    How do I solve these by either substitution/ elimination? I'd also like to know how to solve them using matrices.

    U_n = an^{2}+bn+c=0 Mr F says: So {\color{red}U_n = 0}. Then how can you have non-zero values (below) for the cases n = 1, 2 and 3?
    U_1=4
    U_2=10
    U_3=18

    I need to find the values of the constants a, b, c are.
    None of this makes any sense to me. See the red.


    Do you mean the following?:

    4 = a + b + c .... (1)

    10 = 4a + 2b + c .... (2)

    18 = 9a + 3b + c .... (3)

    The following will give you two equation in a and b:

    Equation (2) - equation (1):

    Equation (3) - equation (1):

    Solve them for a and b. Then use those values in one of the equations to solve for c.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member
    Joined
    Sep 2009
    Posts
    79
    Thanks, from that I got:

    \begin{array}{rcrcrc}a=1\\b=3\\c=0\end{array}

    Is that correct?
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Viral View Post
    Thanks, from that I got:

    \begin{array}{rcrcrc}a=1\\b=3\\c=0\end{array}

    Is that correct?
    Do these answers work when you substitute them into the equations ....?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simultaneous Equations 4 variables, 4 equations
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: December 7th 2011, 05:06 PM
  2. Replies: 1
    Last Post: June 1st 2010, 06:44 AM
  3. Multiple simultaneous equations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 18th 2010, 06:57 AM
  4. Multiple Unknowns in Simultaneous Equations.
    Posted in the Algebra Forum
    Replies: 4
    Last Post: October 25th 2009, 08:28 AM
  5. Replies: 3
    Last Post: February 27th 2009, 08:05 PM

Search Tags


/mathhelpforum @mathhelpforum