Can I use Gauss Elimination if one of my rows is full of 1?

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I'm trying to solve a linear system of equations and I choose to use Gauss Elimination. One of my rows is full of $1$. Can I use the Gauss Elimination? I have to use this row in the first line or in the last line?

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There is nothing special about the matrix with a row of identical nonzero values. The row could be the first row if that helps solving the system.

For example the system $$ x+y=1, 2x+3y=5/2$$is such a system with $x=y=1/2$