Solving Systems 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 if a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if 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

What is the first step in solving a system by substitution?

Back

Make sure at least one equation is solved for one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the graphical interpretation of a system of equations with one solution?

Back

The two lines intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical interpretation of a system of equations with infinite solutions?

Back

The two lines lie on top of each other, representing the same line.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical interpretation of a system of equations with no solution?

Back

The two lines are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the importance of isolating a variable in the substitution method?

Back

Isolating a variable allows for easier substitution into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6