[tex]10x+7y=1 \\
-5x-7y=24 \\ \\
\hbox{solve the first equation for y:} \\
10x+7y=1 \ \ \ |-10x \\
7y=-10x+1 \ \ \ |\div 7 \\
y=\frac{-10x+1}{7} \\ \\
\hbox{substitute the result for y in the second equation:} \\
-5x-7(\frac{-10x+1}{7})=24 \\
-5x-(-10x+1)=24 \\
-5x+10x-1=24 \\
5x-1=24 \ \ \ |+1 \\
5x=25 \ \ \ |\div 5 \\
x=5 \\ \\
y=\frac{-10x+1}{7}=\frac{-10 \times 5+1}{7}=\frac{-50+1}{7}=\frac{-49}{7}=-7 \\ \\
\boxed{(x,y)=(5,-7)}[/tex]
