Systems of Inequalities Word Problems

Front

What is a system of inequalities?

Back

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

Front

How do you represent a word problem as a system of inequalities?

Back

Identify the variables, determine the constraints, and translate the conditions into inequalities.

Front

What does the inequality x + y < 10 represent in a word problem?

Back

It indicates that the total number of items represented by x and y must be less than 10.

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What does the inequality 2x + 3y ≥ 20 represent in a word problem?

Back

It indicates that the total points scored from x two-point shots and y three-point shots must be at least 20.

Front

What is the significance of the '≥' symbol in inequalities?

Back

The '≥' symbol means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to the number.

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What is the significance of the '<' symbol in inequalities?

Back

The '<' symbol means 'less than', indicating that the value must be strictly less than the number.

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How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, shading the region that satisfies all inequalities.

Front

What does it mean if a point is in the solution region of a system of inequalities?

Back

It means that the point satisfies all inequalities in the system.

Front

What is a feasible region in the context of inequalities?

Back

The feasible region is the area on a graph where all the inequalities in a system are satisfied.

Front

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

Back

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