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

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What does it mean for a system of equations to have a unique solution?

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It means there is exactly one set of values for the variables that satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

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

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The graphs of the equations, where the point of intersection represents the solution.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to a system of equations?

Back

The values of the variables that make all equations true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if two lines are parallel in a system of equations?

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The system has no solution because the lines never intersect.

Tags

CCSS.8.EE.C.8B

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What does it mean if two lines coincide in a system of equations?

Back

The system has infinitely many solutions because the lines are the same.

Tags

CCSS.8.EE.C.8A

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How can you determine the solution of a system of equations graphically?

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By finding the point where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

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What is the substitution method in solving systems of equations?

Back

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 where equations are added or subtracted 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 is the significance of the coordinates (x, y) in a solution?

Back

They represent the point on the graph where the two lines intersect, indicating the values of the variables.

Tags

CCSS.8.EE.C.8B