6.1 - 6.2 Number of Solutions & Solutions to Systems of Eq.

Front

If a system of equations has no solution, what does the graph look like?

Back

The graph consists of parallel lines.

Front

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

Back

The solution is the point where the two lines intersect, which is (1, -4).

Front

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

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

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

Back

The graph shows two intersecting lines.

Front

What does it indicate if two lines are skew in a system of equations?

Back

Skew lines do not intersect and are not parallel, indicating no solution.

Front

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

Back

By analyzing the graphs of the equations: intersecting lines have one solution, parallel lines have no solution, and coincident lines have infinitely many solutions.

Front

What is the solution to the system of equations if the graph shows no intersection?

Back

The system has no solution.

Front

What does the term 'infinitely many solutions' imply in a system of equations?

Back

It implies that the equations represent the same line, meaning every point on that line is a solution.

Front

If two lines intersect at a single point, what does that tell us about the system of equations?

Back

It indicates that the system has exactly one solution.

Front

What is the significance of the point (6, -2) in a system of equations?

Back

It represents the unique solution where the two lines intersect.