Write each equation in slope-intercept form. Without...

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $2 x-4 y=5$
$x-2 y=1$

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Key Concepts

Slope-Intercept Form

This form of a linear equation is written as y = mx + b, where m represents the slope of the line and b represents the y-intercept. Converting an equation into this format helps in easily identifying the line’s steepness and point of intersection with the y-axis, which is crucial for graphing and analyzing the line's behavior.

System of Linear Equations

A system of linear equations consists of two or more equations with the same set of variables. The solution to the system is the set of values that satisfy all equations simultaneously. Systems can be solved using methods such as substitution, elimination, or graphing, which reveal how the lines interact—whether they intersect, are parallel, or coincide.

Types of Solutions in a System

In the context of a system of linear equations, there are three possible outcomes: exactly one solution (where the two lines intersect at a single point), no solution (when the lines are parallel and never meet), or an infinite number of solutions (when the lines coincide completely). Determining the slope and y-intercept of each equation aids in identifying which of these scenarios applies by comparing their slopes and intercepts.

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