Number of Solutions to Systems of Equations

Front

If a system of linear equations has one solution, what does this mean about the two lines?

Back

The lines are intersecting.

Front

What is the number of solutions to a system of equations that has exactly one solution?

Back

1 solution.

Front

What is the number of solutions to a system of equations that has infinitely many solutions?

Back

Infinitely Many Solutions.

Front

Why will a system of equations have infinite solutions?

Back

The equations are the same.

Front

How many solutions will a system of equations have if the lines are parallel?

Back

No Solution.

Front

What does it mean if two lines in a system of equations have the same slope but different y-intercepts?

Back

They are parallel and have no solutions.

Front

What does it mean if two lines in a system of equations have the same slope and the same y-intercept?

Back

They are the same line and have infinitely many solutions.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel.

Front

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

Back

Two intersecting lines.

Front

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

Back

Two parallel lines.