Systems of Equations and Their Solutions

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 for a system of equations to have a unique solution?

Back

It means that the graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have no solution?

Back

It means that the graphs of the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, so they overlap completely.

Tags

CCSS.8.EE.C.8A

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

Back

A method 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

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Tags

CCSS.8.EE.B.6

Front

How do you determine if two lines are identical?

Back

Two lines are identical if they have the same slope and the same y-intercept.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines corresponding to each equation plotted on a coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The point of intersection is the solution to the system, where the two lines meet.

Tags

CCSS.8.EE.C.8A