The value of each place-volue osition is 10 times the value of he place to its right and \( \frac{10}{10} \) the value of the place to its left.

The value of each place-value position is 10 times the value of the place to its right and \( \frac{1}{10} \) the value of the place to its left. Let's denote the value of the place to the right as \( x \) and the value of the place to the left as \( y \). Given: 1. The value of each place-value position is 10 times the value of the place to its right: \( x = 10y \) 2. The value of each place-value position is \( \frac{1}{10} \) the value of the place to its left: \( y = \frac{1}{10}x \) We can solve these equations to find the values of \( x \) and \( y \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x=10y\\y=\frac{1}{10}x\end{array}\right.\) - step1: Substitute the value of \(x:\) \(y=\frac{1}{10}\times 10y\) - step2: Simplify: \(y=y\) - step3: Calculate: \(\left(x,y\right) = \left(10y,y\right),y \in \mathbb{R}\) - step4: Alternative Form: \(\textrm{Infinitely many solutions}\) The system of equations has infinitely many solutions. This means that there are multiple values of \( x \) and \( y \) that satisfy the given conditions. Therefore, the value of each place-value position is 10 times the value of the place to its right and \( \frac{1}{10} \) the value of the place to its left, and there are infinitely many solutions for \( x \) and \( y \).