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

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Key Concepts

Linear Systems of Equations

These involve two or more equations containing the same set of variables. The solution to a linear system is a set of values for the variables that simultaneously satisfies all equations. Depending on the system, there can be one solution, no solution, or infinitely many solutions.

Graphing Method

Graphing is a visual approach to solving systems in which each equation is represented as a line on a coordinate plane. The solution to the system is determined by finding the point(s) where the graphs intersect.

Intersection of Graphs

The intersection represents the common solution to the equations in the system. When two lines intersect at a single point, that point is the unique solution to the system. If the lines are parallel, they do not intersect, indicating no solution. If they overlap completely, there are infinitely many solutions.

Set Notation

Set notation is a mathematical notation used to represent solution sets and describe all elements that satisfy a given condition. When a system has a unique solution, the set notation lists only the ordered pair that satisfies both equations; if no or infinitely many solutions exist, the solution is described accordingly in set notation.

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