Chapter 6: Systems of Linear Equations and Matrices

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What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. Solutions are the points where the equations intersect.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How can matrices be used to represent systems of linear equations?

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Matrices can represent the coefficients of the variables in the equations, allowing for efficient manipulation and solution.

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CCSS.HSA.REI.C.8

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What is the purpose of using an inverse matrix in solving systems of equations?

Back

The inverse matrix allows us to isolate the variable matrix, enabling us to find the solution to the system.

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CCSS.HSA.REI.C.9

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What is a coefficient matrix?

Back

A matrix that contains the coefficients of the variables in a system of linear equations.

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CCSS.HSA.REI.C.8

Front

Define augmented matrix.

Back

An augmented matrix is a matrix that includes the coefficients of the variables and the constants from the equations.

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CCSS.HSA.REI.C.8

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

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A consistent system has at least one solution, meaning the equations intersect at one or more points.

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CCSS.8.EE.C.8B

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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Explain the method of substitution in solving systems of equations.

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

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you find the solution to a system of equations using matrices?

Back

You can express the system as a matrix equation, then use matrix operations, including finding the inverse, to solve for the variable matrix.

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CCSS.HSA.REI.C.9