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.
$$\left\{\begin{array}{l}
5 x-y=10 \\
2 x+y=4
\end{array}\right.$$

Key Concepts

Set Notation

Set notation is a concise way to describe the solution set of a system of equations. For a unique solution, set notation specifies the ordered pair that satisfies the system, while for systems with no or infinitely many solutions, it describes the conditions under which the solutions exist.

Intersection of Lines

The intersection point of lines in a graph represents the solution to a system of linear equations when there is exactly one common solution. It is the point where the values of the variables satisfy all the equations simultaneously.

Types of Solutions

Systems of linear equations can have a unique solution, no solution, or infinitely many solutions. These outcomes are determined by the relationships between the slopes and intercepts of the lines representing the equations.

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The goal is to find values for the variables that satisfy all equations simultaneously. This concept is foundational in algebra and forms the basis for understanding more complex mathematical models.

Graphical Method

The graphical method involves plotting each equation on a coordinate plane and identifying the point(s) where the graphs intersect. This visual approach helps in understanding the relationship between equations and in determining the solution(s) to the system.

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