Week 15 Systems of Inequalities FLASHCARD

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 graph an inequality like y > 3?

Back

To graph y > 3, draw a horizontal dashed line at y = 3 (dashed because 3 is not included) and shade the area above the line.

Front

What does the symbol '≥' mean in inequalities?

Back

'≥' means 'greater than or equal to'. It indicates that the value can be greater than or equal to a certain number.

Front

What is the solution to the inequality y ≤ x + 3?

Back

The solution includes all points (x, y) where y is less than or equal to the line represented by y = x + 3.

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 on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it is included in the solution if the inequality is '≥' or '≤', but not if it is '>' or '<'.

Front

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

Back

'>' means greater than (not including the boundary), while '≥' means greater than or equal to (including the boundary).

Front

How do you find the intersection of two inequalities?

Back

Graph both inequalities on the same coordinate plane and identify the region where the shaded areas overlap. This overlapping region represents the intersection.

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 are satisfied. It is typically a polygonal shape.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution if it satisfies all inequalities in the system, meaning it lies within the feasible region.