1. The problem is to solve the system of equations: $$2x + y = 3x - 5y = 13$$ However, this notation is ambiguous. It seems to imply two equations: $$2x + y = 13$$ $$3x - 5y = 13$$ 2. We will solve this system of two linear equations with two variables $x$ and $y$. 3. The system is: $$\begin{cases} 2x + y = 13 \\ 3x - 5y = 13 \end{cases}$$ 4. From the first equation, express $y$ in terms of $x$: $$y = 13 - 2x$$ 5. Substitute $y = 13 - 2x$ into the second equation: $$3x - 5(13 - 2x) = 13$$ 6. Simplify the left side: $$3x - 65 + 10x = 13$$ $$13x - 65 = 13$$ 7. Add 65 to both sides: $$13x - 65 + 65 = 13 + 65$$ $$13x = 78$$ 8. Divide both sides by 13: $$\frac{\cancel{13}x}{\cancel{13}} = \frac{78}{13}$$ $$x = 6$$ 9. Substitute $x=6$ back into $y = 13 - 2x$: $$y = 13 - 2(6) = 13 - 12 = 1$$ 10. The solution to the system is: $$\boxed{(x, y) = (6, 1)}$$