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

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Key Concepts

Set Notation

Set notation is a mathematical language used to clearly and precisely describe sets of numbers, including the solution set of a system of equations. It is commonly used to express the solution as a specific point or collection of points.

System of Linear Equations

These are multiple equations that share common variables and aim to find values for these variables that satisfy all equations simultaneously. The system can have a unique solution, no solution, or infinitely many solutions depending on how the equations relate to one another.

Graphical Representation

Graphing involves plotting each equation on a coordinate plane as a line (or curve, in general cases) to visually identify where the equations intersect, which represents the solution(s) to the system.

Intersection of Graphs

This concept refers to the point(s) at which the graphs of two or more equations cross each other. The intersection represents the set of variable values that satisfy all the equations simultaneously, indicating the solution to the system.

Unique Solution

When the graphs of two linear equations intersect at exactly one point, the system has a unique solution. This single point of intersection corresponds to the unique set of variable values that satisfies both equations.

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