Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

What does the symbol '≥' mean in inequalities?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in inequalities?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (solid for '≥' or '≤', dashed for '>' or '<'). 2. Choose a test point not on the line to determine which side of the line to shade.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.

Front

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

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the feasible region in a system of inequalities?

Back

The feasible region is the area on the graph that represents all possible solutions to the system of inequalities.

Front

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

Back

It means that there is no point that satisfies all inequalities in the system, often indicated by parallel lines that never intersect.

Front

How do you write an inequality from a word problem?

Back

Identify the variables, determine the relationships described, and translate the conditions into an inequality.

Front

What is the maximum number of hours JoAnn can work if she is limited to 15 hours per week?

Back

JoAnn can work a maximum of 15 hours per week, represented by the inequality b + t < 15, where b is babysitting hours and t is tutoring hours.