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.
$$\left\{\begin{array}{l}
x-y=0 \\
y=x
\end{array}\right.$$

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Key Concepts

System of Linear Equations

This concept involves handling multiple equations that share common variables. The goal is to find values for these variables that satisfy all equations simultaneously. Systems can have a unique solution, infinitely many solutions, or no solution at all, depending on how the equations relate to each other.

Graphical Method

The graphical method of solving a system involves plotting each equation on a coordinate plane and identifying the points where the graphs intersect. The intersection point, if it exists, represents the solution that satisfies all the equations in the system.

Intersection of Lines

In the context of systems of linear equations, the intersection of lines represents the set of values that satisfy all of the equations. A single intersection point indicates a unique solution, while overlapping lines indicate an infinite number of solutions, and parallel lines with no points of intersection indicate that no solution exists.

Set Notation

Set notation is a mathematical way to describe the collection of solutions. When expressing the solution of a system, set notation clearly conveys whether there is a unique solution, infinitely many solutions, or no solution by listing the set of all ordered pairs that satisfy the system.

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