Systems of Inequalities

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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.

Tags

CCSS.HSA.REI.D.12

Front

How do you represent a constraint in a system of inequalities?

Back

Constraints are represented as inequalities. For example, if a variable must be less than or equal to a certain value, it is written as x ≤ value.

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What does the inequality 2x + 3y > 100 represent in a real-world context?

Back

It represents a situation where the total value of items (e.g., bracelets and earrings) sold must exceed $100.

Front

What does the inequality x + y ≤ 40 signify?

Back

It signifies that the total number of items (bracelets and earrings) produced cannot exceed 40.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Then, shade the region that satisfies the inequality (above or below the line depending on the inequality sign).

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means greater than and does not include the boundary, while '≥' means greater than or equal to and includes the boundary.

Tags

CCSS.6.EE.B.8

Front

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

Back

The feasible region is the area on a graph where all the inequalities in the system overlap, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

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 the point satisfies all inequalities, it is a solution.

Front

What does it mean if a point lies outside the feasible region?

Back

If a point lies outside the feasible region, it does not satisfy at least one of the inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

The boundary line represents the values where the inequality changes from true to false. It is included in the solution if the inequality is '≤' or '≥'.

Tags

CCSS.HSA.REI.D.12