The following system of equations has a solution \((x,y)\). What is the value of \(y\)? $$ \frac{1}{2}y=4 $$ $$ x-\frac{1}{2}y=2 $$

Summary Submit Skip Question

Note that the first equation only has one solution for \(y\). $$ \frac{1}{2}y=4$$ $$ y=\boxed{8} $$

If we wanted to find the coordinate of intersection or use more familiar methods, we can use substitution. Note that \(\frac{1}{2}y\) exists in both equations, which we can substitute directly.

$$ \colorbox{yellow}{\(\frac{1}{2}y\)}=4 $$ $$ x-\colorbox{yellow}{\(\frac{1}{2}y\)}=2 $$ $$x-4=2$$ $$x=6$$

Substituting back into the second equation,

$$6-\frac{1}{2}y=2$$ $$-\frac{1}{2}y=-4$$ $$y=\boxed{8}$$