Use the idea behind Example 15 with a graphing utility to...

Use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places.
$$
\left\{\begin{aligned} 25 x+61 y-12 z &=25 \\ 18 x-12 y+7 z &=10 \\ 3 x+4 y-& z=-4 \end{aligned}\right.
$$

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Key Concepts

Graphing Utility

A graphing utility refers to a tool, often a calculator or software, that is used to visually plot equations on a coordinate system. This allows one to see the geometric representation of equations and to identify points of intersection, which represent the solutions to the system. It is especially useful for approximating solutions when analytical methods become cumbersome.

Rounding and Approximation

Rounding involves adjusting numerical results to a specified degree of precision, making them easier to interpret and work with, especially when using approximations from graphical or computational methods. This concept is essential when the exact values are either irrational or too complex to use directly, ensuring that the final answers are both accurate and practical.

Systems of Linear Equations

A system of linear equations consists of multiple linear equations that share a common set of variables. The goal is to find a set of values that satisfy all of the equations simultaneously. This concept is critical in various fields of mathematics, science, and engineering as it helps solve problems that involve finding common solutions to different conditions.

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