1. **State the problem:** Solve the system of linear equations: $$x + 2 + y = -2$$ $$3x - y = 5$$ 2. **Rewrite the first equation:** Simplify the first equation by moving the constant term: $$x + y = -2 - 2$$ $$x + y = -4$$ 3. **Express one variable in terms of the other:** From the first equation, $$y = -4 - x$$ 4. **Substitute into the second equation:** Replace $y$ in the second equation: $$3x - (-4 - x) = 5$$ 5. **Simplify the equation:** $$3x + 4 + x = 5$$ $$4x + 4 = 5$$ 6. **Isolate $x$:** $$4x = 5 - 4$$ $$4x = 1$$ 7. **Divide both sides by 4:** $$x = \cancel{\frac{4x}{4}} = \frac{1}{\cancel{4}}$$ 8. **Find $y$ using $x$:** Substitute $x = \frac{1}{4}$ into $y = -4 - x$: $$y = -4 - \frac{1}{4} = -\frac{16}{4} - \frac{1}{4} = -\frac{17}{4}$$ **Final answer:** $$x = \frac{1}{4}, \quad y = -\frac{17}{4}$$