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Here is an example equation:

Solve[{a*x + b*y == c}, {a}]

It gives me:

a -> (c - b*y)/x

To solve the same equation for b, I need to write:

Solve[{a*x + b*y == c}, {b}]

It will give me:

b -> (c - a*x)/y

Similarly, I will have to repeat the steps for all variables like x and y. Is there an easier to tell Mathematica to solve an equation for all variables one by one?

Thanks.

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  • $\begingroup$ Something like: Solve[{ax + by == c}, {#}][[1]] & /@ {a, b, c} & $\endgroup$
    – Daniel Huber
    Commented Oct 26, 2020 at 17:15
  • 2
    $\begingroup$ Flatten@Table[ Solve[a x + b y == c, {z}], {z, {a, b, c, x, y}}] is an easy-to-read method that uses two of the most basic list manipulation functions. $\endgroup$
    – LouisB
    Commented Oct 26, 2020 at 18:04
  • $\begingroup$ Thank you very much @LouisB. Is this feature mentioned somewhere in the documentation? $\endgroup$
    – Real Noob
    Commented Oct 26, 2020 at 18:42
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    $\begingroup$ @RealNoob: you might like to peruse these learning references: mathematica.stackexchange.com/questions/18/… $\endgroup$
    – Moo
    Commented Oct 26, 2020 at 21:41
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    $\begingroup$ Thanks @Moo. :) $\endgroup$
    – Real Noob
    Commented Oct 27, 2020 at 1:52

1 Answer 1

Reset to default
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Generalizing the solution provided by LouisB

Clear["Global`*"]

solve[eqn_Equal] := Module[
  {$z, vars = Variables[Level[eqn, {-1}]]},
  Table[Solve[eqn, {$z}][[1]], {$z, vars}]]

eqn = a x + b y == c;

sol = solve[eqn]

(* {{a -> (c - b y)/x}, {b -> (c - a x)/y}, {c -> a x + b y}, {x -> (c - b y)/
   a}, {y -> (c - a x)/b}} *)

Verifying the solutions

And @@ (eqn /. sol)

(* True *)
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  • $\begingroup$ Thanks @Bob. Could you please provide links to some resources where I can learn more about using Mathemtica in such an advanced manner? I am an absolute beginner in Mathemtica and it seems to be a very powerful tool. :) $\endgroup$
    – Real Noob
    Commented Oct 26, 2020 at 18:50
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    $\begingroup$ All the links are built into Mathematica. Highlight any function or operator and click F1 for help. On the documentation paqes look at the examples and look for the links to Tutorials and Related Guides. $\endgroup$
    – Bob Hanlon
    Commented Oct 26, 2020 at 19:00

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