System of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. Solutions are the values that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

Front

What does the inequality y ≤ x - 3 represent?

Back

It represents all points (x, y) that are below or on the line y = x - 3.

Front

What is the solution set of the inequalities y ≥ -2 and y ≤ x - 3?

Back

The solution set includes all points (x, y) that are above or on the line y = -2 and below or on the line y = x - 3.

Front

What does the inequality y > -x - 1 indicate?

Back

It indicates that y is greater than the line represented by y = -x - 1, meaning all points above this line.

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 the point satisfies all inequalities, it is a solution.

Front

What is the significance of the boundary line in an 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 ≥.

Front

What does the inequality 8x + 25y ≥ 100 represent in a real-world context?

Back

It represents a condition where the total earnings from two jobs must be at least $100.

Front

What is the meaning of the term 'feasible region' in the context of inequalities?

Back

The feasible region is the area on a graph where all the inequalities in a system are satisfied.

Front

What does the inequality y < 2/3x - 3 mean graphically?

Back

It means that the region below the line y = 2/3x - 3 is included in the solution set.