Systems of equations and inequalities

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 the shaded region where the inequalities overlap on a graph.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

What is the difference between a solution to an equation and a solution to an inequality?

Back

A solution to an equation is a specific point; a solution to an inequality is a range of points.

Front

What does the term 'feasible region' refer to in the context of inequalities?

Back

The feasible region is the area on a graph where all constraints (inequalities) are satisfied.

Front

How can you solve a system of equations graphically?

Back

By plotting each equation on the same graph and identifying the intersection point(s).

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, which is 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.

Front

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

Back

A consistent system has at least one solution.