Systems of Equations: Graphing

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The two lines are the same line.

Front

What is the solution to the system of equations represented by the point (6, -2)?

Back

The point (6, -2) is the intersection of the two lines, representing the solution to the system.

Front

How many solutions does the system have if the equations are y=5x+3 and y=5x-2?

Back

No Solution, because the lines are parallel.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines intersect at a single point.

Front

What is the solution to the system of equations represented by the point (1, -4)?

Back

The point (1, -4) is the intersection of the two lines, representing the solution to the system.

Front

What are the characteristics of parallel lines in the context of systems of equations?

Back

Parallel lines have the same slope but different y-intercepts, resulting in no solutions.

Front

What does it mean for two lines to be coincident in a system of equations?

Back

Coincident lines are the same line, leading to infinitely many solutions.

Front

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

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.

Front

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

Back

The intersection point represents the solution to the system, where both equations are satisfied.