In Exercises 11-42, solve each system by graphing. If there...

In Exercises $11-42,$ solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets.
$$\left\{\begin{array}{l}
x+2 y=2 \\
x-y=2
\end{array}\right.$$

Key Concepts

Set Notation

Set notation is a standardized way of expressing mathematical solutions clearly and concisely. In the context of systems of equations, it is used to denote the solution set, whether it is a unique point, an empty set for no solution, or a set of points for infinite solutions. This notation ensures clarity in communicating the results of the system analysis.

Systems of Linear Equations

This concept involves dealing with multiple linear equations that share common variables. The goal is to find values of the variables that satisfy all the equations simultaneously. It is a foundational topic in algebra and is used to model and solve real-world problems where different constraints must be met concurrently.

Graphing Method

Graphing is a visual method of solving systems of equations by plotting the corresponding lines on a coordinate plane. The solution to the system corresponds to the point or points where the lines intersect. This method is especially useful for understanding the behavior of equations and provides an intuitive illustration of the solution.

Intersection Point

The intersection point represents the unique solution to a system of linear equations when the lines are not parallel. It is the set of values for the variables that satisfies each equation in the system. Understanding intersections is crucial in determining whether a system has a unique solution, no solution (parallel lines), or infinitely many solutions (coincident lines).

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