Answer
The solution to this system of equations is $(\frac{1}{2}, \frac{1}{4})$.
Work Step by Step
We can solve for $y$ in terms of $x$ in the first equation so that we can use this value for $y$ to substitute into the second equation. Let's solve for $y$ in the first equation:
$4y = 2x$
Divide both sides by $4$ to solve for $y$:
$y = \dfrac{2x}{4}$
Reduce the fraction by dividing both numerator and denominator by $2$:
$y = \dfrac{x}{2}$
Now, we use this value for $y$ to substitute into the first equation:
$2x + \frac{x}{2} = \frac{x}{2} + 1$
Let us subtract $\frac{x}{2}$ from both sides of the equation so they can cancel each other out:
$2x = 1$
Divide both sides by $2$ to solve for $x$:
$x = \dfrac{1}{2}$
Now that we have a value for $x$, we can substitute it into the first equation to solve for $y$:
$4y = 2(\frac{1}{2})$
$4y = 1$
Divide both sides by $4$ to solve for $y$:
$y = \frac{1}{4}$
The solution to this system of equations is $(\frac{1}{2}, \frac{1}{4})$.
