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 of a system of equations?

Back

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

Front

What is an inequality?

Back

A mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

How do you graph a linear inequality?

Back

Graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Front

What is the solution to a system of inequalities?

Back

The set of all points that satisfy all inequalities in the system, often represented by the overlapping shaded regions.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is 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 does it mean for a system to be consistent?

Back

A system is consistent if it has at least one solution.