https://file.aiquickdraw.com/mathbot/file/1727439135176sdmywewb.jpg

The image shows three equations:

1. \( 12.9 = 5b + 10a + 30c \)
2. \( 37.1 = 10a + 30b + 100c \)
3. \( 130 = 30a + 100b + 354c \)

We need to solve this system of equations to find the values of \(a\), \(b\), and \(c\).

Let me solve it for you.The solution to the system of equations is:

- \( a = 0.251 \) (approximately)
- \( b = -0.003 \) (approximately)
- \( c = 0.347 \) (approximately)

Would you like more details on the steps? Feel free to ask any questions.

Here are five related questions you might explore:

1. What method is used to solve a system of linear equations with three variables?
2. How can you verify the solution to a system of equations?
3. What happens if a system of equations has no solution?
4. How do you interpret negative values for variables in a real-world context?
5. Can such systems of equations be solved graphically?

**Tip:** When solving systems of equations, substitution and elimination methods are commonly used if you're solving by hand. For larger systems, matrix methods like Gaussian elimination are efficient.

Solve the system of linear equations and find the values of a, b, and c.

Discover how to solve a system of linear equations with three variables. This guide covers essential algebraic techniques including matrix methods and Cramer's rule, suitable for high school level studies.

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