1. **State the problem:** Solve the system of equations: $$\begin{cases} x^2 + xy = 2 \\ x + y = 1 \end{cases}$$ 2. **Use substitution method:** From the second equation, express $y$ in terms of $x$: $$y = 1 - x$$ 3. **Substitute $y$ into the first equation:** $$x^2 + x(1 - x) = 2$$ 4. **Simplify the equation:** $$x^2 + x - x^2 = 2$$ $$\cancel{x^2} + x - \cancel{x^2} = 2$$ $$x = 2$$ 5. **Find $y$ using $x=2$:** $$y = 1 - 2 = -1$$ 6. **Check the solution:** First equation: $$x^2 + xy = 2^2 + 2 \times (-1) = 4 - 2 = 2$$ Second equation: $$x + y = 2 + (-1) = 1$$ Both equations are satisfied. **Final answer:** $$\boxed{(x, y) = (2, -1)}$$