Solving systems of equations by substitution

Front

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 when a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Tags

CCSS.8.EE.C.8B

Front

What is the significance of the statement '2 = 2' in solving systems of equations?

Back

It indicates that the equations are equivalent, leading to infinite solutions.

Tags

CCSS.8.EE.C.8B

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

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

How do you determine if a system of equations has one solution?

Back

If the equations represent lines that intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

Back

The solution can be found at the point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the first step in using the substitution method?

Back

Solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if two equations are dependent?

Back

They represent the same line and have infinite solutions.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two equations are independent?

Back

They represent different lines and can have one solution or no solution.

Tags

CCSS.8.EE.C.8A