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step 1 To solve this system of equations, I will be using the elimination method. Now, to use the elimi

Solve each system of equations. If the system has no...

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The goal is to find values for the variables that satisfy every equation simultaneously. In the context of a two-variable system, the solution can be a single unique point (if the lines intersect), infinitely many solutions (if the lines are coincident), or no solution (if the lines are parallel and distinct).

Elimination Method

The elimination method is a technique used to solve systems of linear equations by adding or subtracting the equations to eliminate one of the variables. Once one variable is eliminated, the resulting single-variable equation can be solved directly, and then this result is substituted back into one of the original equations to determine the other variable.

Consistency and Inconsistency

A system of linear equations is termed consistent if there is at least one solution; this includes cases with a unique solution or infinitely many solutions. It is called inconsistent if no solution exists, which occurs when the equations represent parallel lines that never intersect. Recognizing inconsistency is important in determining whether a system has a meaningful solution or not.

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