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The image contains a system of three equations involving variables \( x_1 \), \( x_2 \), and \( x_3 \). The system is as follows:

\[
\frac{x_1}{2} + \frac{1}{3}\left( \frac{x_1}{2} + \frac{x_2}{3} + \frac{x_3}{6} \right) = \frac{1}{2}(x_1 + x_2 + x_3)
\]

\[
\frac{2x_2}{3} + \frac{1}{3}\left( \frac{x_1}{2} + \frac{x_2}{3} + \frac{x_3}{6} \right) = \frac{1}{3}(x_1 + x_2 + x_3)
\]

\[
\frac{5x_3}{6} + \frac{1}{3}\left( \frac{x_1}{2} + \frac{x_2}{3} + \frac{x_3}{6} \right) = \frac{1}{6}(x_1 + x_2 + x_3)
\]

### To solve the system:

1. Simplify each equation.
2. Use substitution or elimination to find the values of \( x_1 \), \( x_2 \), and \( x_3 \).

Would you like me to walk through these steps and solve the system?

The image contains a system of three equations involving variables x1, x2, and x3. The system is as follows: 
 1. x1/2 + (1/3)(x1/2 + x2/3 + x3/6) = (1/2)(x1 + x2 + x3) 
 2. (2x2)/3 + (1/3)(x1/2 + x2/3 + x3/6) = (1/3)(x1 + x2 + x3) 
 3. (5x3)/6 + (1/3)(x1/2 + x2/3 + x3/6) = (1/6)(x1 + x2 + x3)

This page explains how to solve a system of linear equations with variables x1, x2, and x3. It walks through simplifying the equations and using substitution or elimination methods. Suitable for Grades 10-12, this example covers fundamental algebraic methods.

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