Verified Answer :

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\(14x-2y=46 \\ -7x+y=-23 \\ \\ \hbox{solve the 2nd equation for y:} \\ -7x+y=-23 \\ y=7x-23 \\ \\ \hbox{substitute 7x-23 for y in the 1st equation:} \\ 14x-2(7x-23)=46 \\ 14x-14x+46=46 \\ 14x-14x=46-46 \\ 0=0 \\ \\ \boxed{\hbox{infinitely many solutions}}\)

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