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

Here's how to solve the system of equations: $$\begin{cases} y = 3 + x \\ 4y = 2x \end{cases}$$ We can use the substitution method. Step 1: Substitute the expression for 'y' from the first equation into the second equation. Since $$y = 3 + x$$, we can substitute this into the second equation: $$4(3 + x) = 2x$$ Step 2: Solve for 'x'. Expand the left side: $$12 + 4x = 2x$$ Subtract 4x from both sides: $$12 = -2x$$ Divide both sides by -2: $$x = -6$$ Step 3: Solve for 'y'. Now that we have the value of x, we can substitute it back into either of the original equations to find 'y'. Let's use the first equation: $$y = 3 + x$$ $$y = 3 + (-6)$$ $$y = -3$$ Solution Therefore, the solution to the system of equations is: $$x = -6, y = -3$$ Answer: x = -6, y = -3