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

Slope-Intercept Form

This is a way to express a linear equation in the form y = mx + b, where m represents the slope (or the steepness and direction of the line) and b represents the y-intercept (the point where the line crosses the y-axis). Converting equations into this form makes it easier to understand and compare the properties of different linear equations.

System of Linear Equations

A system of linear equations consists of two or more linear equations that are considered together. The solution of the system is the set of values that simultaneously satisfy all equations. Analyzing the system involves determining whether the lines represented by the equations intersect, are parallel, or coincide.

Types of Solutions in Linear Systems

Linear systems can have exactly one solution, no solution, or an infinite number of solutions. A unique solution arises when the lines intersect at exactly one point, no solution occurs when the lines are parallel (having the same slope but different y-intercepts), and infinitely many solutions occur when the equations represent the same line (coincident lines).

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