7.7 All types of Systems Review

Front

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.

Front

How do you convert a system of equations into an augmented matrix?

Back

To convert a system of equations into an augmented matrix, write the coefficients of the variables in rows and the constants in the last column.

Front

Back

The solution is (2, 5).

Front

What does it mean for a system of equations to be consistent?

Back

A system of equations is consistent if it has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system of equations is inconsistent if it has no solutions.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is a solution set in the context of systems of equations?

Back

A solution set is the set of all possible solutions to a system of equations.

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane; the point(s) where the lines intersect represent the solution(s).

Front

What is a dependent system of equations?

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A dependent system has infinitely many solutions, where the equations represent the same line.