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.
$$\left\{\begin{array}{l}
x+y=6 \\
y=-3
\end{array}\right.$$

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Key Concepts

Set Notation for Solutions

Set notation is a precise way to express the solution to a system of equations. It delineates whether the system has a unique solution, no solution, or infinitely many solutions by clearly specifying the values of the variables or the condition they satisfy.

Systems of Linear Equations

A system of linear equations consists of two or more equations that describe straight lines in a coordinate plane. The goal is to find the set of variable values that satisfy all equations simultaneously. This concept is foundational in algebra and analytic geometry, as it illustrates how multiple conditions can limit or determine the possible solutions.

Graphical Method

The graphical method involves plotting each equation on the same coordinate plane and identifying their intersections. This approach not only provides a visual representation of the solutions but also helps in understanding scenarios where lines intersect at a single point (unique solution), are parallel (no solution), or coincide (infinitely many solutions).

Intersection of Lines

The intersection point of two lines represents the solution to the system of linear equations when the lines meet at a single point. This concept underscores the idea that the common point satisfies all equations simultaneously and is a key indicator of the system’s solution status.

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