Results 1 to 7 of 7

Math Help - Help using two equations to solve each other

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    Colorado
    Posts
    8

    Help using two equations to solve each other

    Help using two equations to solve each other
    (1) a/2+b=1
    (2) 3a-b/3=31/2

    Im lost on what to do here. I know I need to pick the easier equation to produce a equaling so I choose equation 1
    what im trying to do is first clearing the fractions in eq1 I listed below what my thinking looks like but I know its wrong Please help

    a/2+b=1 multiply both a/2 by 2 and the right side by 2 and i get
    a+b=2 then I want to find a so I -b
    a=2-b

    in the second eq i substitute for a now
    3a-b/3=31/2
    3(2-b)-b/3=31/2 now i clear the brackets
    6-3b+b/3=31/2 now i clear the fractions bymultiplying both sides by 3. 3x b/3 and the right side 31/2=15.5 x3
    6-3b+b=15.5x3 simplify to
    6-3b+b=46.5 now i get the bs alone
    -3b+b=40.5 merge the bs
    -2b=40.5
    -b=40.5/2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645

    Re: Help using two equations to solve each other

    Hello, Scryer!

    \begin{array}{ccccc}\frac{a}{2}+b&=&1 & [1] \\ 3a-\frac{b}{3} &=&\frac{31}{2} & [2] \end{array}

    I see that you are using the Substitution Method.

    First, I would get rid of the fractions.

    \begin{array}{ccccccc}\text{Multiply [1] by 2:} & a + 2b &=& 2 & [3] \\ \text{Multiply [2] by 6:} & 18a - 2b &=& 93 & [4] \end{array}

    Solve [1] for a\!:\;a + 2b \:=\:2 \quad\Rightarrow\quad a \:=\:2 - 2b

    Substitute into [2]: . 18(2-2b)-2b \:=\:93 \quad\Rightarrow\quad 36 - 36b - 2b \:=\:93

    . . . . . . . . . . . . . . . \text{-}38b \:=\:57 \quad\Rightarrow\quad b \:=\:\tfrac{57}{\text{-}38}\quad\Rightarrow\quad \boxed{b \:=\:\text{-}\tfrac{3}{2}}

    Substitute into [1]: . a + 2\left(\text{-}\tfrac{3}{2}\right)-2 \:=\:2 \quad\Rightarrow\quad a - 3 \:=\:2 \quad\Rightarrow\quad \boxed{a \:=\:5}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2012
    From
    Colorado
    Posts
    8

    Re: Help using two equations to solve each other

    I see you are multiplying through i out i forgot to do that thanks and I see how you would multiply (1) by 2 But how did you figure to multiply (2) by 6 I seem to be having trouble with that
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    910
    Thanks
    27

    Re: Help using two equations to solve each other

    Quote Originally Posted by Scryer View Post
    I see you are multiplying through i out i forgot to do that thanks and I see how you would multiply (1) by 2 But how did you figure to multiply (2) by 6 I seem to be having trouble with that

    That was done to get 2b in the second equation and have b eliminated in summing equation 1 and 2
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2012
    From
    Colorado
    Posts
    8

    Re: Help using two equations to solve each other

    but how did you decide to multiply (1) by 2 and (2) by 6
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Help using two equations to solve each other

    Those are the lowest common denominators. (1) has one denominator of 2 , so multiplying by 2 will clear it, while (2) has a denominator of 2 and a denominator of 3 and the LCM of 2 and 3 is 6, so 6 is the smallest number that will clear both denominators.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2012
    From
    Colorado
    Posts
    8

    Re: Help using two equations to solve each other

    Ah I see I forgot completly about the LCM thanks to all of you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Is it possible to solve these equations?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 8th 2011, 02:43 PM
  2. How should I solve these equations?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 21st 2011, 04:20 AM
  3. Solve the following equations
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 10th 2008, 05:22 PM
  4. solve equations
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 9th 2008, 07:04 PM
  5. solve equations
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 24th 2006, 09:40 AM

Search Tags


/mathhelpforum @mathhelpforum