x+y+z=1
x+y-z=1
x+y=1
You asked:
Solve the system of equations:\[\begin{aligned}x + y + z &= 1\\x + y - z &= 1\\x + y &= 1\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}x &= 1 - y\\z &= 0\end{aligned}$$\(y\) is a free variable.