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In this image, you are asked to solve a system of linear equations using a software program or graphing utility. The system is given as follows:

\[
\begin{aligned}
123.5x + 61.3y - 32.4z &= -315.29, \\
54.7x - 45.6y + 98.2z &= 199.93, \\
42.4x - 89.3y + 12.9z &= 40.09.
\end{aligned}
\]

You are tasked with solving this system of equations for \(x\), \(y\), and \(z\) in terms of a parameter \(t\). If the system has no solutions, or if it's dependent on a parameter, that must be indicated.

Would you like me to:

1. Solve this system step-by-step, explaining each part?
2. Check if it's consistent or dependent on a parameter \(t\)?
3. Provide tips on how to use a graphing utility for solving this system?

Let me know how you'd like to proceed, and feel free to upload any additional data or questions!

Here are five related questions:
1. How do you determine if a system of equations has infinite solutions?
2. What is Gaussian elimination, and how can it be used to solve a system of equations?
3. How does a parameter \(t\) affect the general solution of a system of equations?
4. Can every system of linear equations be solved using a graphing utility?
5. What methods exist to verify the consistency of a system of equations?

**Tip**: When using a graphing utility to solve systems of equations, always double-check that you've entered the coefficients correctly to avoid calculation errors.

Solve the following system of linear equations using a software program or graphing utility:
123.5x + 61.3y - 32.4z = -315.29
54.7x - 45.6y + 98.2z = 199.93
42.4x - 89.3y + 12.9z = 40.09
Solve for x, y, and z in terms of a parameter t, if applicable.

Learn how to solve a system of three linear equations using a graphing utility or software program. The problem involves finding solutions for x, y, and z, and explores parameterization techniques, Gaussian elimination, and row echelon form. Suitable for college-level linear algebra students.

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