Relatable Reversal Of Digits

Algebra Level 2

AB=2BA1\large \overline{\color{#D61F06}{A}\color{#3D99F6}{B}}=2\overline{\color{#3D99F6}{B}\color{#D61F06}{A}}-1

Let AB\overline{\color{#D61F06}{A}\color{#3D99F6}{B}} and BA\overline{\color{#3D99F6}{B}\color{#D61F06}{A}} be 2-digit integers that satisfy the equation above. Find AB\overline{\color{#D61F06}{A}\color{#3D99F6}{B}}.

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