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

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.

Front

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).

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.

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.

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.

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 '≥'.