Verified Answer :

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

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