In Problems 71-74, use the idea behind Example 15 with a...

In Problems 71-74, use the idea behind Example 15 with a graphing utility to solve the following systems of equations. Round answers to two decimal places.
$\left\{\begin{aligned} 25 x+61 y-12 z & =21 \\ 18 x-12 y+7 z & =7 \\ 3 x+4 y-z & =-2\end{aligned}\right.$

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Key Concepts

Rounding and Approximation

Rounding and approximation are techniques used to simplify numerical answers to a desired level of precision. This is especially important when using digital tools like graphing utilities, where the exact solution might be a long or non-terminating decimal. Rounding to a specified number of decimal places ensures clarity and consistency in the final answer.

Intersection of Graphs

The intersection of graphs is the point where two or more curves or lines meet on a graph. In the context of a system of equations, this intersection point corresponds to the common solution, meaning it provides the values of the variables that make every equation true simultaneously.

Systems of Linear Equations

A system of linear equations consists of multiple linear equations with several variables. The goal is to find a set of values for the variables that simultaneously satisfies all the equations. This concept is fundamental in algebra and is the basis for many applications in various fields such as physics, economics, and engineering.

Graphical Methods

Graphical methods involve plotting equations on a coordinate system to visually identify their point of intersection. This approach provides an intuitive understanding of the solution, as the intersection represents the set of values that satisfies all the equations in the system.

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