A.3F System of Equations Manually

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What is a system of equations?

Back

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

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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 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 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

Front

How can you graphically represent a system of equations?

Back

By plotting the equations on a coordinate plane and finding the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

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

Back

It means the system is inconsistent, as the lines will never intersect and have no solutions.

Tags

CCSS.8.EE.C.8A

Front

What is the point of intersection in a system of equations?

Back

The point where the graphs of the equations meet, representing the solution to the system.

Tags

CCSS.8.EE.C.8B