Solving system of equations gives empty output, but gives result when reduced

Questions
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1

I want solve equation group below, but you can see the result return a {},
but when i reduce the equation group like this , it can give a solution(Seeing in the image),
why is this ?

mathematica.png
mathematica.png686×410 7.54 KB

2

you have two Delta_l1

3

Please put your code in code blocks, not as images. Code blocks allow other members to copy and paste your code into Mathematica. You can find out how to do that, and many more useful things, by reading How to post .

4

I want solve equation group below, but you can see the result return a {},
but when i reduce the equation group like this , it can give a solution(Seeing in the image),
why is this ?

mathematica.png
mathematica.png686×410 7.54 KB

5

20241006_170048.jpg
20241006_170048.jpg739×221 40 KB

6

Try it with a space or a * between a and x and between b and y, etc.

But if you want ax to be a single variable and not the product of a and x, then I have no idea what you wanted to ask. It would be helpful if you included a question that could be answered.

In future, I think it would be better to start a new discussion to discuss a new problem. I wouldn’t introduce a new problem into an old discussion.

7

Five equations in three unknowns, you are asking for trouble. However, you get solvability conditions in terms of the parameters:

eqs = {fn1*Sin[a] - fn2*Sin[a] == 0,
   fn3 + 2 fn1*Cos[a] - f == 0,
   dl1 == dl3*Cos[a],
   dl1 == fn1*1/(e1*a1*Cos[a]),
   dl3 == fn3*1/(e3*a3)};
vars = {fn1, fn2, fn3};
sol0 = Solve[eqs[[{1, 2, 4}]], vars]
eqs /. sol0[[1]]
Solve[eqs /. sol0[[1]]]