Without graphing, decide. a. Are the graphs of the equations...

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}y=3 \\ x=-4\end{array}\right.$

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Key Concepts

System of Linear Equations

Systems of linear equations consist of two or more linear equations involving the same set of variables. The goal is to determine the values of these variables that satisfy every equation in the system concurrently. Depending on the relationships between the equations, the system may have one unique solution, infinitely many solutions, or no solution.

Unique Solution in a System

A system of linear equations has a unique solution when there is exactly one set of variable values that satisfies all the equations. This corresponds to the situation where the graphs of the linear equations intersect at a single point, indicating that the equations are independent and not parallel or coincident.

Intersection of Horizontal and Vertical Lines

Horizontal and vertical lines demonstrate a special case in coordinate geometry. A horizontal line represents a constant y-value while a vertical line represents a constant x-value. These two lines are always perpendicular and intersect at exactly one point, which is the unique solution for the system composed of such equations.

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