Types of Solutions

Front

What is a solution in the context of equations?

Back

A solution is a value or set of values that satisfies an equation, making it true.

Front

What does it mean if an equation has infinite solutions?

Back

It means that there are countless values that can satisfy the equation, often occurring when two equations represent the same line.

Front

What is the definition of a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

What does it mean if a system of equations has no solution?

Back

It means that there is no set of values that can satisfy all equations in the system, often occurring when the lines are parallel.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions.

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, as the equations represent the same line.

Front

What is an independent system of equations?

Back

An independent system has exactly one solution, where the lines intersect at a single point.

Front

How can you determine if two equations are equivalent?

Back

Two equations are equivalent if they have the same solution set.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation shows the lines of the equations on a coordinate plane, where intersections represent solutions.