When solving for \(y\), we typically want to eliminate or substitute a value for \(x\). Solving for \(x\) in the second equation,
$$y=2x$$
$$\frac{1}{2}y=x$$
Substituting this value into the first equation,
$$ \frac{1}{2}(2x+y)=\frac{21}{2}$$
$$ \frac{1}{2}\Big(2\left(\frac{1}{2}y\right)+y\Big)=\frac{21}{2}$$
$$ \frac{1}{2}(y+y)=\frac{21}{2}$$
$$ \frac{1}{2}(2y)=\frac{21}{2}$$
$$ 2y=21 $$
$$ y=\boxed{\frac{21}{2}}$$
Like the previous question, we can make the equations more manageable before beginning the process of elimination or substitution.
$$ \frac{1}{2}(2x+y)=\frac{21}{2}$$
$$ \Big(2\Big)\Big( \frac{1}{2}(2x+y) \Big)=\frac{21}{2} \Big( 2 \Big) $$
$$ 2x+y=21$$