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.
$$\left\{\begin{array}{l}
y=0 \\
y=5
\end{array}\right.$$

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Key Concepts

Set Notation

Set notation is a concise method of representing the solution set of a system. For systems with no solution, the empty set (?) is used, indicating that there are no values satisfying all equations in the system.

Inconsistent Systems

An inconsistent system is one in which there are no solutions because the graphs of the equations do not intersect. This typically occurs when the equations represent parallel lines, as they maintain a constant distance and never meet.

Systems of Linear Equations

A system of linear equations consists of two or more equations that share common variables. The solution to the system is the set of values that satisfies all the equations simultaneously, often found by identifying the point(s) of intersection of their graphs.

Graphing Linear Equations

Graphing linear equations involves plotting lines on the coordinate plane using their algebraic expressions. This process helps visualize the relationship between the variables and is a fundamental tool in understanding and solving systems of equations.

Intersection of Graphs

The intersection of graphs representing linear equations is the point where the lines meet. This common point represents the solution of the system. If the lines do not intersect or coincide, the system is either inconsistent or has infinitely many solutions, respectively.

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