Systems of Linear Equations

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What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to isolate a variable in an equation?

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To manipulate the equation so that the variable is on one side by itself.

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted 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?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

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The lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of linear equations?

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The solution is the point(s) where the lines intersect on a graph.

Tags

CCSS.8.EE.C.8A

Front

How do you determine the best method to solve a system of equations?

Back

Consider the form of the equations; if one is already solved for a variable, use substitution; if coefficients can easily be eliminated, use elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is an ordered pair in the context of systems of equations?

Back

A pair of numbers (x, y) that represents the solution to the system, indicating the point of intersection.

Tags

CCSS.8.EE.C.8A

Front

What is the standard form of a linear equation?

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Ax + By = C, where A, B, and C are constants.