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. $3 x-3 y=9$
$2 x-2 y=-4$

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Key Concepts

Slope-Intercept Form

This is a linear equation format written as y = mx + b, where m represents the slope indicating the steepness and direction of the line, and b represents the y-intercept where the line crosses the y-axis. It simplifies understanding the behavior of the line and facilitates graphing it.

System of Linear Equations

A set of two or more equations that share the same variables. The solution to a system is found where all equations are satisfied simultaneously, which corresponds to the intersection point(s) of the lines represented by those equations.

Consistency and Dependency

Systems of equations are classified based on their solution sets. A consistent system has at least one solution, while an inconsistent system has none. When the equations of a system represent the same line, the system is dependent and has infinitely many solutions.

Parallel and Coincident Lines

When two lines have the same slope but different y-intercepts, they are parallel and do not intersect, meaning the corresponding system of equations has no solution. Conversely, if the lines not only share the same slope but also the same y-intercept, they are coincident, leading to infinitely many solutions as they lie on top of each other.

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