Systems of Equations-Graphing Substitution, and Inspection

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 one solution?

Back

It means the lines intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means the lines 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 the lines coincide, or are the same line.

Tags

CCSS.8.EE.C.8A

Front

How can you solve a system of equations using graphing?

Back

By plotting the equations on a graph and identifying the point(s) of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is substitution in the context of solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of the solution (1, -4)?

Back

It is the point where the two lines intersect on a graph.

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the slopes of two lines in a system of equations?

Back

If the slopes are equal and the y-intercepts are different, the system has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the first step in solving a system of equations using substitution?

Back

Isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if two lines are graphed over each other?

Back

It indicates that the system of equations has infinitely many solutions.

Tags

CCSS.8.EE.C.8A