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,

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