Multivariable system of equations

Questions
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1

Hello all,

I just started using Mathematica and am trying to solve this simple system of equations. I get empty set as an answer somehow. I know how to do it with hand but I want to know how to work it out in Mathematica so I can use the software for complicated system of equations. Please help me to understand what’s wrong.

2

Quick guess – you are using what you intend to be subscripted variables, but in fact are only using “box representation”, in other words, your expression for x_5 is not in fact a Symbol.

Retry using x5 for x_5, et cet.

3

I still get the same empty braces for the answer. :frowning:

4

It looks like you have 6 equations and 7 unknowns:

Solve[{10.109*w - d*200 - 0.788*500 - 1.231*4*x5 + 16.296*101.8 - 1.231*x4 == 0,
  101.8 - 4*x5 - 2*x3 - x4 - x2 == 0,
  y1 + w - 500 - 200 == 0,
  x5 == 0.563*x3,
  x4 == x2,
  1.5*x4 == x5},
 {x2, x3, x4, x5, y1, w, d}]

which results in

{{x2 -> 7.63771, x3 -> 20.3491, x4 -> 7.63771, x5 -> 11.4566, 
  w -> 700. - 1. y1, d -> 41.3771 - 0.050545 y1}}
5

Per documentation, Solve only gives generically correct solutions. This means that if equations are forced upon parameters (non-Solve variables), then solutions forcing those are removed. In this case, as only one variable d was specified to solve for, all others are regarded as parameters. The following variant will give what I think is the expected result.

Solve[{10.109*w - d*200 - 0.788*500 - 1.231*4*Subscript[x, 5] + 
    16.296*101.8 - 1.231*Subscript[x, 4] == 0, 
  101.8 - 4*Subscript[x, 5] - 2*Subscript[x, 3] - Subscript[x, 4] - 
    Subscript[x, 2] == 0, Subscript[y, 1] + w - 500 - 200 == 0, 
  Subscript[x, 5] == 0.563*Subscript[x, 3], 
  Subscript[x, 4] == Subscript[x, 2], 
  1.5*Subscript[x, 4] == Subscript[x, 5]}]