Solve the system, or show that it has no solution. If the...

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example $6 .$
$$
\left\{\begin{array}{c}{0.2 x-0.2 y=-1.8} \\ {-0.3 x+0.5 y=3.3}\end{array}\right.
$$

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Key Concepts

System of Linear Equations

A system of linear equations is a collection of one or more equations involving the same set of variables, where each equation represents a straight line in two dimensions or a plane in higher dimensions. Solving the system means finding all the variable values that satisfy all of the equations simultaneously.

Elimination Method

The elimination method is a systematic process used to solve systems of linear equations by canceling out one variable at a time. This is typically done by multiplying the equations by appropriate factors so that when they are added or subtracted, one variable is eliminated. The process is then repeated for the remaining variables, leading to a reduced system that is easier to solve.

Consistency and Types of Solutions

When dealing with systems of linear equations, it is important to determine whether the system is consistent (has at least one solution) or inconsistent (has no solution). Consistent systems can have a unique solution, indicating that the underlying equations intersect at a single point, or infinitely many solutions, indicating that the equations represent the same line or plane. Understanding these scenarios is crucial for correctly interpreting and expressing the solution.

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