If $(x - 1, y + 2) = (y - 2, 2x + 1)$, then $(x, y)$ is—

Matching components gives $x - 1 = y - 2$ and $y + 2 = 2x + 1$. From the first, $x = y - 1$; substituting into the second gives $y + 2 = 2(y-1) + 1$, so $y = 3$ and $x = 2$.