give me a short-solve system of equations problem with x=1/2 y=1/3 and z=1/8

Here's a system of equations where the solution is \( x = \frac{1}{2}, y = \frac{1}{3}, z = \frac{1}{8} \):

\[
\begin{aligned}
2x + 3y + 8z &= 2 \\
4x - y + 16z &= 3 \\
x + 6y - 4z &= 1
\end{aligned}
\]

This system of equations can be verified by substituting \( x = \frac{1}{2}, y = \frac{1}{3}, z = \frac{1}{8} \) into each equation. Would you like a detailed explanation of how this works?

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Here are 5 related questions for further practice:
1. Solve the system of equations \( x + y + z = 1 \), \( 2x - y + z = 0 \), and \( x - 2y + 3z = 2 \).
2. What happens if you change one of the coefficients in the system?
3. Can a system have more than one solution?
4. How can you tell if a system of equations has no solution?
5. What is an inconsistent system of equations?

**Tip:** Always check your solution by substituting the values back into the original equations.

give me a short-solve system of equations problem with x=1/2, y=1/3, and z=1/8

This problem demonstrates how to solve a system of linear equations with specific solutions: x = 1/2, y = 1/3, and z = 1/8. Explore the algebraic concepts of systems of equations, including substitution and linear combination methods. Suitable for Grades 9-12.

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