Solving Systems Word Problems with Matrices

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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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.

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns, used to represent a system of equations.

Front

How can matrices be used to solve systems of equations?

Back

Matrices can be used to represent systems of equations in a compact form, allowing for the application of matrix operations to find solutions.

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What is the purpose of the augmented matrix?

Back

An augmented matrix combines the coefficients and constants of a system of equations into a single matrix, facilitating the use of row operations to solve the system.

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What is row reduction?

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Row reduction is a method used to simplify a matrix to its row echelon form or reduced row echelon form, making it easier to solve the system of equations.

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What is the difference between consistent and inconsistent systems?

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A consistent system has at least one solution, while an inconsistent system has no solutions.

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What is a dependent system?

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

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How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What is the substitution method?

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The substitution method involves solving one equation for a variable and substituting that expression into another equation.