Solve each system of equations by graphing. If the system is inconsistent or the equations are d

step 1 In this problem, we're being asked to solve the given system of equations by graphing. So to do

Solve each system of equations by graphing. If the system is...

Key Concepts

Consistent and Inconsistent Systems

A consistent system of equations is one that has at least one solution, whether that solution is unique (a single intersection) or infinite (coincident lines). An inconsistent system, on the other hand, has no solution because the graphs of the equations do not intersect, indicating that the equations are contradictory.

Intersection Point

The intersection point is the coordinate point where the graphs of the equations meet, representing the common solution to all equations in the system. This is crucial in understanding consistent systems, where a unique intersection indicates a unique solution.

Dependent Equations

Dependent equations occur when two or more equations in a system are essentially the same, leading the graphs to overlap completely. This results in infinitely many solutions since every point on the line satisfies each equation, distinguishing them from independent equations which have a unique intersection.

Systems of Linear Equations

This concept involves working with two or more linear equations that are solved simultaneously. A solution to the system is a set of variable values that satisfy every equation in the system, and it is a foundational concept in algebra that leads to understanding intersections, consistency, and dependence among equations.

Graphical Method

The graphical method is a visual approach for solving systems of equations by plotting each equation on a coordinate system and identifying where the graphs intersect. This method helps to visualize the relationship between the equations, such as where they cross (indicating a unique solution) or if they are parallel or coincident.

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