Systems of Linear Equations

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What is a system of linear equations?

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A system of linear equations is two or more linear equations that share the same variables.

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CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

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

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A consistent and independent system has exactly one solution, where the lines representing the equations intersect at a single point.

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CCSS.8.EE.C.8A

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What is an inconsistent system of equations?

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An inconsistent system is a system of equations that has no solution, meaning the lines are parallel and never intersect.

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CCSS.8.EE.C.8A

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What is the graphical method for solving a system of linear equations?

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The graphical method involves plotting the equations on a graph and identifying the point(s) where they intersect.

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CCSS.8.EE.C.8B

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What is the substitution method in solving systems of equations?

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

Tags

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 other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

A consistent system has at least one solution, which can be either one solution (independent) or infinitely many solutions (dependent).

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CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

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A dependent system is a system of equations that has infinitely many solutions, meaning the equations represent the same line.

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CCSS.8.EE.C.8B

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How can you determine if two equations are independent?

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Two equations are independent if their graphs intersect at exactly one point, indicating a unique solution.

Tags

CCSS.8.EE.C.8B

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What is the importance of the slope in linear equations?

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The slope indicates the steepness of the line and the direction of the relationship between the variables in the equation.

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CCSS.8.EE.B.5