1. **State the problem:** Solve the equation $2x - y + 2z = 13$ for one variable or analyze it as a linear equation in three variables. 2. **Formula and rules:** This is a linear equation in three variables $x$, $y$, and $z$. Such equations represent planes in 3D space. To solve for one variable, isolate it on one side. 3. **Isolate $y$:** $$2x - y + 2z = 13$$ Subtract $2x$ and $2z$ from both sides: $$-y = 13 - 2x - 2z$$ 4. **Cancel the negative sign:** Multiply both sides by $-1$: $$\cancel{-}y \cancel{=} - (13 - 2x - 2z)$$ $$y = -13 + 2x + 2z$$ 5. **Final answer:** $$\boxed{y = 2x + 2z - 13}$$ This expresses $y$ in terms of $x$ and $z$.