How Many Solutions?

Front

What does it mean when an equation has infinitely many solutions?

Back

It means that no matter what constant is substituted in for the variable, the equation is always true.

Front

What is the definition of no solution in the context of equations?

Back

No matter what constant is substituted in for the variable, the equation will never be true.

Front

How can you identify if a system of equations has infinitely many solutions?

Back

If the equations are equivalent or represent the same line, they will have infinitely many solutions.

Front

What is a unique solution in a system of equations?

Back

A unique solution occurs when the equations intersect at exactly one point.

Front

What is the graphical representation of no solution?

Back

Two parallel lines that never intersect.

Front

What is the graphical representation of infinitely many solutions?

Back

Two lines that lie on top of each other, representing the same line.

Front

What is the difference between consistent and inconsistent systems of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is a dependent system of equations?

Back

A system where the equations are equivalent, leading to infinitely many solutions.

Front

What is an independent system of equations?

Back

A system where the equations have exactly one solution.

Front

How do you determine the number of solutions for a system of linear equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.