## SUBJECT II

Determine all pairs of non-zero digits $(x, y)$ with the property that $\xlongequal[\overline{x y x y x y}]{\overline{y x y y x}}=\frac{4}{7}$.

Mathematical Gazette
## Solution:

![](https://cdn.mathpix.com/cropped/2024_06_07_f344a73543ba19f21944g-2.jpg?height=77&width=1419&top_left_y=1910&top_left_x=300)

![](https://cdn.mathpix.com/cropped/2024_06_07_f344a73543ba19f21944g-2.jpg?height=114&width=689&top_left_y=2011&top_left_x=314) ..... $2 p$
Obtaining the relation $2 x=y$ ..... $2 p$
Finalization: $(x, y) \in\{(1,2),(2,4),(3,6),(4,8)\}$ ..... $1 p$