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What is an augmented matrix?

Back

An augmented matrix is a matrix that represents a system of linear equations, including the coefficients of the variables and the constants from the equations.

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How do you write a system of equations as an augmented matrix?

Back

To write a system of equations as an augmented matrix, list the coefficients of the variables in each equation as rows and the constants as an additional column.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What is the solution to a system of equations?

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The solution to a system of equations is the set of values for the variables that make all equations true.

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What is a consistent system of equations?

Back

A consistent system of equations has at least one solution.

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solutions.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, as the equations represent the same line or plane.

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How can you determine if a system of equations has no solution?

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A system of equations has no solution if the equations represent parallel lines that never intersect.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection point(s) of the lines or planes represented by the equations.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.