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. $\frac{x}{3}+\frac{y}{4}=1$
$4 x+3 y=12$

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Key Concepts

Types of Solutions in Linear Systems

Linear systems can be classified based on the relationship between the equations: if the lines intersect at exactly one point, the system has a unique solution; if the lines are parallel and do not meet, the system has no solution; and if the lines lie on top of each other, the system has infinitely many solutions.

Slope-Intercept Form

This form of a linear equation is written as y = mx + b, where m represents the slope and b represents the y-intercept. It is used to easily identify the steepness of the line and where it crosses the y-axis, which simplifies graphing and comparison of different linear equations.

Systems of Linear Equations

A system of linear equations involves two or more linear equations with the same variables. The solution to the system is the set of variable values that satisfy all equations simultaneously. Analysis of these systems can reveal whether the lines intersect at a single point, do not intersect at all, or coincide completely.

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