Solving Systems of Equations by Graphing

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Parallel lines never intersect because they have the same slopes.

Tags

CCSS.8.EE.C.8B

Front

What is the result when two lines in a system of equations are parallel?

Back

The system has no solution.

Tags

CCSS.8.EE.C.8B

Front

If two lines overlap each other, what can be said about the solutions of the system?

Back

The system has infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = 2x + 1?

Back

The solution is (x, y) where x can be any real number, indicating infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

How can you determine the number of solutions in a system of equations by graphing?

Back

By observing the intersection points of the lines: no intersection means no solution, one intersection means one solution, and overlapping lines mean infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations represented by the lines y = x + 2 and y = -x + 4?

Back

The solution is (1, 3).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means the lines intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations with no solutions?

Back

The lines are parallel and do not intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The lines overlap each other completely.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B