Systems of Equations and Inequalities

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point in a coordinate plane.

Tags

CCSS.HSA.CED.A.3

Front

What does it mean for an ordered pair to be a solution to a system of equations?

Back

It means that the ordered pair satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you check if an ordered pair is a solution to a system?

Back

Substitute the values of the ordered pair into each equation and see if the equations hold true.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

A system that has infinitely many solutions, where the equations represent the same line.

Tags

CCSS.8.EE.C.8B