Identifying Solutions to Systems of Equations

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 no solution?

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinite solutions?

Back

The lines are the same, meaning they overlap completely.

Tags

CCSS.8.EE.C.8A

Front

How do you find the solution to a system of equations graphically?

Back

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

Tags

CCSS.8.EE.C.8B

Front

What is the slope of a line?

Back

The ratio of the rise (vertical change) to the run (horizontal change) between two points on the line.

Tags

CCSS.8.EE.B.5

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Tags

CCSS.8.EE.B.6

Front

How can you determine if two lines are perpendicular?

Back

If the product of their slopes is -1.

Tags

CCSS.8.EE.B.6

Front

What is the substitution method in solving systems of equations?

Back

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

What is the elimination method in solving systems of equations?

Back

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