2=y-x
10=y+z
8=z+x
You asked:
Solve the system of equations:\[\begin{aligned}2 &= y - x\\10 &= y + z\\8 &= z + x\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}x &= 8 - z\\y &= 10 - z\end{aligned}$$
\(z\) is a free variable.