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 .
$\left\{\begin{array}{l}x=5 \\ y=-2\end{array}\right.$

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Key Concepts

Graphical Representation of Equations

Linear equations can be represented as lines on the coordinate plane. The intersection of these lines corresponds to the solution of the system. Understanding this graphical representation helps in determining the nature of the solution without explicitly solving the equations algebraically.

Properties of Vertical and Horizontal Lines

Vertical and horizontal lines are special cases in the coordinate plane. A vertical line, given by an equation like x = a, has an undefined slope, while a horizontal line, given by y = b, has a slope of zero. Their intersection, when they are not overlapping, occurs exactly at one distinct point.

Systems of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The solutions to the system are the points that satisfy all equations simultaneously, which can result in a unique solution when the lines intersect at a single point, no solution when the lines are parallel, or infinitely many solutions when the lines coincide.

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