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

Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations that share the same set of variables. Such a system seeks values for the variables that satisfy every equation simultaneously, representing lines in the coordinate plane whose intersection, if any, corresponds to the solution of the system.

Graphing Method

The graphing method involves drawing the lines represented by each equation on a coordinate plane and then visually identifying their point of intersection. This approach not only aids in finding the solution but also helps in understanding the relationships between the equations such as whether they intersect, are parallel, or coincide.

Types of Solutions in Systems of Equations

When graphing a system of equations, the nature of the intersection determines the solution type. A unique solution occurs when the lines intersect at exactly one point, infinite solutions occur when the lines are identical (coinciding), and no solution exists when the lines are parallel and never intersect.

Set Notation for expressing Solutions

Set notation is a concise way to express the collection of solutions to an equation or system of equations. It is used to denote a unique solution by listing the coordinate pair, an infinite number of solutions by describing the relationship satisfied by all points on the line, or the absence of a solution by indicating an empty set.

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