[tex]\begin{cases} 3x+5y=50\\ x+5y=31\\[-0.5em] \hrulefill\\ x+5y=31\\ x = 31-5y \end{cases}\qquad \implies \stackrel{\textit{substituting in the 1st equation}}{3(31-5y)+5y=50} \\\\\\ 93-15y+5y=50\implies 93-10y=50\implies -10y=-43 \\\\\\ y=\cfrac{-43}{10}\implies \boxed{y=\cfrac{43}{10}} \\\\[-0.35em] ~\dotfill\\\\ x = 31-5y\implies x = 31-5\left( \frac{43}{10} \right)\implies x = 31-\cfrac{43}{2}\implies \boxed{x = \cfrac{19}{2}}[/tex]
[tex]\stackrel{~\hfill \textit{\large total for 7x + 5y}}{7\left( \cfrac{19}{2} \right)+5\left( \cfrac{43}{10} \right)\implies \cfrac{133}{2}+\cfrac{43}{2}\implies \cfrac{133+43}{2}\implies \cfrac{176}{2}\implies 88}[/tex]
