Review Systems of Equations and Inequalities

Front

What is a dependent system of equations?

Back

A system of equations that has infinitely many solutions, where the equations represent the same line.

Front

What is an inconsistent system of equations?

Back

A system of equations that has no solution, where the lines are parallel.

Front

What is an independent system of equations?

Back

A system of equations that has exactly one solution, where the lines intersect at a single point.

Front

What does it mean if a solution reads 3=4?

Back

It indicates no solution exists for the system, as the statement is false.

Front

What does it mean if a solution reads 4=4?

Back

It indicates that there are infinitely many solutions, as the statement is always true.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point into both equations; if it satisfies both, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where their intersection points represent solutions.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is a solution to a system of inequalities?

Back

A set of values that satisfies all inequalities in the system, often represented as a shaded region on a graph.