Solve the system of equations: $$ \begin{cases} 2x + y = 1 \\ 4x - 2y = -9 \end{cases} $$

Let's solve the system of equations step by step. Step 1: Express one variable in terms of the other from the first equation. From the first equation, we can express $$y$$ in terms of $$x$$: $$y = 1 - 2x$$ Step 2: Substitute the expression for $$y$$ into the second equation. Substitute $$y = 1 - 2x$$ into the second equation: $$4x - 2(1 - 2x) = -9$$ Step 3: Simplify and solve for $$x$$. Expand and simplify the equation: $$4x - 2 + 4x = -9$$ $$8x - 2 = -9$$ $$8x = -9 + 2$$ $$8x = -7$$ $$x = -\frac{7}{8}$$ Step 4: Substitute the value of $$x$$ back into the expression for $$y$$. Substitute $$x = -\frac{7}{8}$$ into $$y = 1 - 2x$$: $$y = 1 - 2\left(-\frac{7}{8}\right)$$ $$y = 1 + \frac{14}{8}$$ $$y = 1 + \frac{7}{4}$$ $$y = \frac{4}{4} + \frac{7}{4}$$ $$y = \frac{11}{4}$$ Step 5: Write the solution as an ordered pair $$(x, y)$$. The solution to the system of equations is $$x = -\frac{7}{8}$$ and $$y = \frac{11}{4}$$. Answer: $$\left(-\frac{7}{8}, \frac{11}{4}\right)$$