Systems of Inequalities Word Problems & Review

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 region where the graphs of the inequalities overlap.

Front

How do you represent a word problem involving money and items sold as inequalities?

Back

Identify the cost of each item and the total amount needed. For example, if bracelets cost $2 (x) and earrings cost $3 (y), and you need at least $100, the inequality is 2x + 3y ≥ 100.

Front

What does the inequality x + y ≤ 40 represent in a jewelry-making scenario?

Back

It represents the maximum number of pieces of jewelry (bracelets and earrings) that can be made, which is 40.

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What is the difference between a solution to a system of equations and a system of inequalities?

Back

A solution to a system of equations is a specific point that satisfies all equations, while a solution to a system of inequalities is a range of points that satisfy all inequalities.

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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 all inequalities are satisfied, the point is a solution.

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What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it satisfies the equation of the line. For ≤ or ≥ inequalities, the point is included in the solution; for < or >, it is not.

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What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions that indicate all possible solutions, with boundary lines separating the regions.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all the possible solutions that satisfy the inequalities in the system.

Front

How do you solve a system of inequalities graphically?

Back

Graph each inequality on the same coordinate plane, shade the appropriate regions, and identify the overlapping shaded area as the solution.

Front

What is a feasible region in the context of systems of inequalities?

Back

The feasible region is the area on the graph where all the shaded regions overlap, representing all possible solutions to the system.