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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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean to solve a system of equations?

Back

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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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

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CCSS.HSA.REI.C.8

Front

How can matrices be used to solve systems of equations?

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Matrices can be used to represent systems of equations, and methods like Gaussian elimination or matrix inversion can be applied to find solutions.

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CCSS.HSA.REI.C.9

Front

What is the purpose of using variables in word problems?

Back

Variables are used to represent unknown quantities in word problems, allowing us to set up equations to find solutions.

Tags

CCSS.6.EE.B.6

Front

What is the first step in solving a word problem using a system of equations?

Back

The first step is to define the variables and what they represent in the context of the problem.

Tags

CCSS.8.EE.C.8C

Front

How do you set up a system of equations from a word problem?

Back

Identify relationships and constraints in the problem, then translate them into equations using the defined variables.

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CCSS.HSA.CED.A.3

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients represent the numerical values that multiply the variables, indicating the relationship between the variables in the equations.

Tags

CCSS.HSA.REI.C.8

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect, indicating that there are no values that satisfy all equations.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning any point on the line is a solution.

Tags

CCSS.8.EE.C.8B