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.
$$\left\{\begin{array}{l}
y=x+5 \\
y=-x+3
\end{array}\right.$$

Key Concepts

Solution Sets

The solution set of a system of equations is the collection of all ordered pairs (or tuples) that satisfy every equation in the system. When expressing the solution in set notation, braces {} are used to enclose the unique solution, all the solutions in the case of infinitely many solutions, or to indicate that no solution exists if the lines are parallel.

Intersection of Lines

The intersection of lines is the point where the graphs of two linear equations cross each other. This point represents the solution to the system of equations, as it provides the values for the variables that satisfy both equations simultaneously. If the lines intersect at one point, the system has a unique solution.

Graphing Linear Equations

Graphing linear equations involves plotting the lines represented by the equations on the coordinate plane using their slopes and y-intercepts. This visual representation helps in identifying the point of intersection or in determining if the lines are parallel or coincident, which in turn indicates whether there is a unique solution, no solution, or infinitely many solutions.

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. In the context of graphing, each equation represents a straight line on the coordinate plane, and solving the system involves finding where these lines intersect, which represents the set of variable values that satisfy all the equations simultaneously.

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