Unit 5 Graphing Systems of Inequalities

Front

What is a solution to a system of inequalities?

Back

A solution is a set of values that satisfies all inequalities in the system.

Front

How do 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 true, the point is a solution.

Front

What does it mean when the graph of an inequality is shaded above the line?

Back

It indicates that all points above the line satisfy the inequality (e.g., y ≥ mx + b).

Front

What does the symbol '≥' represent in an inequality?

Back

It means 'greater than or equal to', indicating that the value can be either greater than or equal to a certain number.

Front

What does the symbol '>' represent in an inequality?

Back

It means 'greater than', indicating that the value must be strictly greater than a certain number.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 with a dashed line, then shade below the line.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region where the shaded areas of all inequalities overlap.

Front

How can you identify a system of inequalities from a graph?

Back

Look for the boundary lines and determine the shading direction for each inequality.

Front

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

Back

If the line is solid, the point is included in the solution; if dashed, it is not included.