Set::write: Tag Plus in <something> is Protected

Question

If I have this equation:

x+y=27
xy=180

I want to solve it using:

Solve[{x+y==27,xy==180},{x,y}]

However this results in the following errors:

• Set::write: Tag Plus in x+y is Protected. >>
• Solve::svars: Equations may not give solutions for all "solve" variables. >>

Why? And how do I fix this?

Solution

If you just run the line

Solve[{x + y == 27, x y == 180}, {x, y}]

then everything runs fine and you find {{x -> 12, y -> 15}, {x -> 15, y -> 12}}.

The error you see is because somewhere you've got a statement like

In[1]:= x + y = 27

During evaluation of In[1]:= Set::write: Tag Plus in x+y is Protected. >>

Out[1]= 27

Where the head of x + y is Plus which is a protected symbol and can't be naively given new definitions. It might be that you have some weird definition hiding somewhere, in which case, it's simplest to restart the kernel and try again.

The moral of the story is that = (Set) is not the same as == (Equal).

Comments

[Simon]

This question is about the syntax of Mathematica language and not about the use of the software, so is probably more suitable for stackoverflow.

[MariusMatutiae]

There is site for the Mathematica program, it is mathematica.stackexchange.com