Solve the system of equations: $$\begin{cases} 2x = -8 + 5y \\ 2x + 3y = -4 \end{cases}$$

Let's solve the given system of equations step-by-step: $$\begin{cases} 2x = -8 + 5y \\ 2x + 3y = -4 \end{cases}$$ First, let's express $$2x$$ from the first equation: $$2x = -8 + 5y$$ Now, substitute this expression for $$2x$$ into the second equation: $$(-8 + 5y) + 3y = -4$$ Simplify the equation: $$-8 + 5y + 3y = -4$$ Combine like terms: $$8y - 8 = -4$$ Add 8 to both sides of the equation: $$8y = -4 + 8$$ $$8y = 4$$ Divide both sides by 8: $$y = \frac{4}{8}$$ $$y = \frac{1}{2}$$ Now that we have the value of $$y$$, we can substitute it back into the expression for $$2x$$: $$2x = -8 + 5y$$ $$2x = -8 + 5(\frac{1}{2})$$ $$2x = -8 + \frac{5}{2}$$ To combine these terms, we need a common denominator, which is 2. So, convert -8 to a fraction with denominator 2: $$2x = -\frac{16}{2} + \frac{5}{2}$$ $$2x = \frac{-16 + 5}{2}$$ $$2x = \frac{-11}{2}$$ Now, divide both sides by 2 to solve for $$x$$: $$x = \frac{-11}{2} \div 2$$ $$x = \frac{-11}{2} \cdot \frac{1}{2}$$ $$x = \frac{-11}{4}$$ So we have found the values for $$x$$ and $$y$$: $$x = -\frac{11}{4}$$ $$y = \frac{1}{2}$$ Thus, the solution to the system of equations is $$x = -\frac{11}{4}$$ and $$y = \frac{1}{2}$$. Answer: $$x = -\frac{11}{4}, y = \frac{1}{2}$$