[tex] \bf \begin{cases}\boxed{y}=\cfrac{1}{4}x+7\\\\y=\cfrac{1}{2}x+5\end{cases}\implies \stackrel{y}{\boxed{\cfrac{1}{4}x+7}}=\stackrel{y}{\cfrac{1}{2}x+5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{x+28=2x+20}\\\\\\8=x\qquad \qquad \stackrel{\textit{using x = 8 in the first equation}}{y=\cfrac{1}{4}(8)+7}\implies y=2+7\implies y=9 [/tex]
if you ever wonder why multiplying both sides the LCD of all equations, is just to get rid of the fractions.
