\(\int^{x+y=15}_{\frac{7}{50}x+\frac{1}{10}y=13}\)<=>\(\int^{y=15-x}_{\frac{7}{50}x+\frac{1}{10}\left(15-x\right)=13}\)<==>\(\int^{y=15-x}_{\frac{7}{50}x+\frac{15}{10}-\frac{1}{10}x=13}\)<=>\(\int^{y=15-x}_{\frac{1}{25}x=13-\frac{15}{10}}\)<=>\(\int^{x=\frac{575}{2}}_{y=15-\frac{575}{2}=-\frac{545}{2}}\)
\(\frac{7}{50}x+\frac{5}{50}y=13\Leftrightarrow\frac{2}{50}x+\frac{5}{50}\left(x+y\right)=13\Leftrightarrow\frac{1}{25}x=13-15.\frac{1}{10}=\frac{23}{2}\Leftrightarrow x=\frac{575}{2}\)
=> y= -545/2