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.
$$\left\{\begin{array}{l}
y=3 x-1 \\
y=3 x+2
\end{array}\right.$$

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more equations that share the same set of variables. The goal is to find the variable values that satisfy all the equations simultaneously. Such systems can have a unique solution, no solution, or infinitely many solutions.

Graphing Linear Equations

Graphing is a visual method for solving systems of equations by plotting each equation on the coordinate plane and determining where the graphs intersect. This method provides an intuitive understanding of the relationships between equations and their solutions.

Parallel Lines

When two lines have the same slope but different y-intercepts, they are parallel and never intersect. In the context of a system of linear equations, parallel lines indicate that there is no solution because no single pair of values satisfies both equations at the same time.

Set Notation

Set notation is a mathematical shorthand for describing the solution set of an equation or system of equations. It provides a clear and concise way to express whether there is a unique solution, no solution, or infinitely many solutions.

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