Systems of Inequalities

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.

Tags

CCSS.8.EE.C.8B

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

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

Back

A system has an infinite number of solutions if the inequalities overlap in such a way that there are countless points that satisfy all inequalities.

Tags

CCSS.HSA.REI.D.12

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

Tags

CCSS.HSA.REI.D.12

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. If the inequality is strict (e.g., > or <), the line is dashed; if it is inclusive (e.g., ≥ or ≤), the line is solid.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line. 2. Use a dashed line for strict inequalities and a solid line for inclusive inequalities. 3. Shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does the solution set of a system of inequalities look like?

Back

The solution set is the intersection of the shaded regions of all inequalities, representing all points that satisfy every inequality in the system.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between a strict and non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

Tags

CCSS.6.EE.B.8

Front

How can you tell if a point is above or below a line in a linear inequality?

Back

If the point satisfies the inequality (e.g., y > mx + b), it is above the line; if it does not satisfy it, it is below the line.

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.

Tags

CCSS.HSA.REI.D.12