Systems of Equations and Inequalities (Graphs) #1

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 graphical representation consists of shaded regions that indicate the solutions to the inequalities.

Front

How do you determine if a point is in the solution set of a system of inequalities?

Back

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

Front

What is the overlap of shaded regions in a system of inequalities?

Back

The overlap represents the set of points that satisfy all inequalities in the system.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

What does it mean for a point to be outside the solution set of a system of inequalities?

Back

A point is outside the solution set if it does not satisfy at least one of the inequalities.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line represents the points where the inequality changes from true to false.

Front

How can you graph a system of equations?

Back

By plotting each equation on the same coordinate plane and finding the intersection points.

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, while a solution to an inequality is a range of points.