a=b+c
c=d+e
a=f
d+e=f
b+c=d+e
You asked:
Solve the system of equations:\[\begin{aligned}a &= b + c\\c &= d + e\\a &= f\\d + e &= f\\b + c &= d + e\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}a &= f\\b &= 0\\c &= f\\d &= f - e\end{aligned}$$
\(f\) is a free variable.