In Exercises 66-69, determine whether each statement is true...

In Exercises $66-69$, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
If a linear system has graphs with equal $y$ -intercepts, the system must have infinitely many solutions.

Key Concepts

Slope and Y-Intercept

The slope of a line describes its steepness and direction, while the y-intercept is the point where the line crosses the y-axis. Together, these parameters uniquely determine the line. Even if two lines share the same y-intercept, differing slopes mean they intersect only once, while identical slopes and y-intercepts imply the lines are coincident.

Linear Systems

A linear system is a set of two or more linear equations involving the same variables. The goal is to find a set of values that satisfies all equations simultaneously. These systems can have a unique solution, infinitely many solutions, or no solution at all.

Graphical Representation of Linear Equations

Graphing linear equations results in straight lines in the coordinate plane. The point(s) where these lines intersect represent the solutions to the system. This graphical approach provides a visual method to understand the behavior of the equations and the nature of their solution set.

Solution Types of Linear Systems

Depending on how the graphs of the equations relate to each other, a linear system can have a unique solution (when the lines intersect at a single point), infinitely many solutions (when the lines are identical or coincident), or no solution (when the lines are parallel and distinct). Understanding these conditions is key to correctly determining the nature of the solution set.

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