Systems of Equations and Inequalities Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Front

What is the graphical representation of a system of inequalities?

Back

The solution set is represented by shaded regions on a graph, indicating where the inequalities overlap.

Front

What does a dashed line represent in a graph of an inequality?

Back

A dashed line indicates that points on the line are not included in the solution set.

Front

What does a solid line represent in a graph of an inequality?

Back

A solid line indicates that points on the line are included in the solution set.

Front

How do you check if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation to see if they hold true.

Front

What is the substitution method for solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.