Simultaneous equations and calculator

Discussion in 'Math' started by Steve1992, Sep 11, 2012.

  1. Steve1992

    Thread Starter Senior Member

    Apr 7, 2006
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    My calculator can solve simultaneous in the format:

    ax + by = c

    2 unknowns: x,y
    coefficients a,b,c

    Is it possible to transform this equation into that format:

    (x - y)/2 = y/4


    I feel Ive tried most permutations.
     
  2. Sparky49

    Active Member

    Jul 16, 2011
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    417
    Can you get it into y=mx+c?

    Hint, get everything on one line.
     
  3. Steve1992

    Thread Starter Senior Member

    Apr 7, 2006
    100
    0
    So I should solve it graphically?
     
  4. Sparky49

    Active Member

    Jul 16, 2011
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    Well, if it is a simultaneous equations you're doing, you need two equations.

    This one looks simple enough, but it really depends on the other equation.

    At this stage it seems like you just need a pen and paper. :)


    Can you put it into y=mx+c?
     
  5. WBahn

    Moderator

    Mar 31, 2012
    17,777
    4,805
    What "permutations"?

    Just multiply it out and gather terms:

    (x-y)/2 = (y/4)

    (x-y)/2 = (x/2) - (y/2) = (y/4)

    (x/2) - (y/2) - (y/4) = 0

    (x/2) - y[(1/2) + (1/4)] = 0

    x(1/2) - y(3/4) = 0

    x(1/2) + y(-3/4) = 0

    So, this is of the form ax + by = c with a=1/2, b=-3/4, and c=0.

    Q.E.D.

    Until you are comfortable solving simultaneous equations without a calculator, don't use a calculator to solve simultaneous equations. If you do, then you are not using the calculator as a tool, but rather as something to do your thinking for you.

    I suspect that this might be at the root of your problem with the algebra in this case -- you've let calculators do too much of your work for you and are not therefore proficient with the basic arithmetic skills needed to perform the algebraic manipulations.

    If so, throw the calculator in a draw, or only use it to get sines and logs and the like (i.e., punching in the numbers to evaluate a final result and, even then, only when it is not reasonable to do so by hand or in your head). Work the math symbolically by hand every change you get.
     
    Steve1992 and justtrying like this.
  6. justtrying

    Active Member

    Mar 9, 2011
    329
    354
    If you are solving a system of equations, please do it by hand and use substitution or elimination to get the answer, you will have it quicker than trying to change all equations into the form where you can punch the coefficients into the calculator. There is also less chance of a mistake. You can check your answer by plugging in the results into all equations or by solving it using another method. Graphing also works, but sometimes only approximate solution can be obtained. If you do not master solving it on your own, by hand, you will be a slave of your calculator, nothing more. You will also be better prepared for what is yet to come...
     
  7. Sparky49

    Active Member

    Jul 16, 2011
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    417
    Or... We could just do it for him.
     
  8. Steve1992

    Thread Starter Senior Member

    Apr 7, 2006
    100
    0
    Your right. I was looking for short cuts.
    Im doing this as an interest more than leading anywhere.
     
  9. Sparky49

    Active Member

    Jul 16, 2011
    834
    417
    Whenever you come across equations like this, always start by getting them on one level - much easier that way.

    Then work to get them into a form you are familiar with, in this case y=mx+c.

    Then re-arrange to get them to where you need to. :)
     
  10. WBahn

    Moderator

    Mar 31, 2012
    17,777
    4,805
    Yeah. Short cuts have their place, but they can become a crutch real easy. In some respects I went through high school at an optimal time -- just a year or two before and all calculations were by hand or, at best, with a four function calculator. So lots of slide rules and trig/log tables. A few years after I went through and most of the students had used calculators from a very early age and weren't expected to do more than token calculations by hand and weren't even shown what a trig/log table was. I was in the transition. Scientific calculators had finally come down in price so that they were reasonable affordable (~$40 in 1980$) and so were used in chem and physics classes to crank numbers, but the rest of the curriculum, and all of the math curriculum, were still completely centered on hand calculations. We didn't use slide rules (but I learned how to use circular slide rules as a pilot), but were forced to develop solid math skills that were well practiced. But my freshman year in college I got addicted to an HP-41 and by the end of the spring semester caught myself pulling out the calculator to add two two-digit numbers and realized that doing it in my head really was a bit of a struggle I couldn't believe how quickly and thoroughly those basic skills atrophy. So right then and there I decided that I would use the calculator only for things for which it was reasonable to use it for, meaning that it was unreasonable to expect someone with solid arithmetic skills to do without one. I do lot's of computations on paper and have taken a bit of grief from colleagues over the years. But I have stayed pretty true to that line for three decades and it has served me well. More than once I have been able to spot errors in project specifications or reviews solely because I could run estimates in my head with sufficient confidence to point it out on the spot.
     
    Adamf001 likes this.
  11. Sparky49

    Active Member

    Jul 16, 2011
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    My maths teacher was telling me about a time where a graphic calculator would get you an A at A-level.

    Pay the price of a graphic calculator and you fly through the exam...

    Wonderful times... :D
     
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