$x+y=100x-y\text{ and }100x-y=100$

$x = \frac{200}{101} = 1\frac{99}{101} \approx 1.98019802$
$y = \frac{9900}{101} = 98\frac{2}{101} = 98.01980198019803$

$y = \frac{9900}{101} = 98\frac{2}{101} = 98.01980198019803$
$x = \frac{200}{101} = 1\frac{99}{101} = 1.9801980198019802$