A mathematical puzzle about the manipulation and solution of equations. Use with [mathematics]

Algebra is the study of mathematical symbols and the rules for manipulating these symbols. Puzzles involving equations, variables, polynomials, vectors and/or matrices should include this tag. General algebra questions are off-topic but can be asked on our sister site Mathematics Stack Exchange.

Example: Some birds are sitting in two trees. The birds in the first tree say to the others: "If one of you comes to our tree, our number will be twice your number." The birds in the second tree said: "If one of you comes here, our number will be equal to yours." How many birds are in each tree? (Answer: $7$ and $5$).