Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Front

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

Back

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

Front

What is the graphical representation of a system of inequalities?

Back

The solution set is represented by the overlapping shaded regions of the inequalities.

Front

What does 'y ≤ -2x + 5' represent graphically?

Back

It represents all points below or on the line y = -2x + 5.

Front

What does 'y > 2x + 7' indicate about the solution set?

Back

It indicates that the solution set includes points above the line y = 2x + 7.

Front

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

Back

Substitute the point into each inequality and check if all inequalities are satisfied.

Front

What is the significance of the boundary line in a linear inequality?

Back

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

Front

What does it mean if a system of inequalities has no solution?

Back

It means that the shaded regions of the inequalities do not overlap.

Front

What does it mean if a system of inequalities has infinite solutions?

Back

It means that there are infinitely many points that satisfy all inequalities.

Front

How can you identify a point that is NOT a solution to a system of inequalities?

Back

A point is NOT a solution if it fails to satisfy at least one inequality.