# Simultaneous equations with 3 variables

Discussion in 'Mathematics and Physics' started by Overclocked, Oct 18, 2006.

1. ### ljcoxWell-Known Member

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Ax+By=C ------1
Dx+Ey=F -- ---2

Multiply 1 by D

ADx+BDy=CD -----3

Multiply 2 by A

ADx+AEy=AF-----4

Subtracting 3 from 4 gives

0x+AEy-BDy = AF - CD

So (AE-BD)y = AF - CD

y = (AF - CD)/(AE - BD)

To solve for x, substitute this value for y in your fourth equation.

Now to express y in the form you wrote above, divide the top and bottom lines by A

y = {F - C(D/A)}/{E - (D/A)B}

For 3 variables, you do the same but you need more steps.

Firstly, reduce the three 3 variable equations to two 2 variable ones by eliminating one variable. Then do what I did above to solve for the 2 remaining variables.

Then you can substitute these into one of the original equations and solve for the third variable.

Last edited: Feb 24, 2007
2. ### thushyNew Member

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I would say that if you know there exist unique solutions then probably the easiest way solve the set of equations is Cramer's rule

3. ### salman007New Member

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i will go for cramer rule to solve these problems

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5. ### swood30New Member

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TI-83 is the way to go! Engr undergrads surely know how to add and subtract by now. In your case, it's a big waste of time to work it out algebraically.

6. ### aljamriMember

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do not worry, he will use it after graduation, but for know he needs to know how the things can be done, and how to apply the rules.

7. ### PommieWell-Known MemberMost Helpful Member

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He has probably already graduated as he asked the question 3 years ago.

Mike.

8. ### SydneyNew Member

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This is a standar problem with first year students in university here in Australia even though it is supposed to be taught before hand. I have to often teach this as an extra, yet when they see it students tell me "it is simple" then discover how to manipulate formula.

Look outside the square then square it