Systems of Inequalities

Front

What is a system of inequalities?

Back

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 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 set 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 that are above the line y = -2 and below or on the line y = x - 3.

Front

What does the symbol '≥' mean in inequalities?

Back

It means 'greater than or equal to'.

Front

What does the symbol '≤' mean in inequalities?

Back

It means 'less than or equal to'.

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 is the significance of the boundary line in a graph of an inequality?

Back

The boundary line separates the solution set from the non-solution set. Points on the line are included if the inequality is ≤ or ≥.

Front

What does the inequality y > -2x + 3 represent?

Back

It represents all points (x, y) that are above the line y = -2x + 3.

Front

What is the graphical representation of the inequality y < 3x?

Back

It is a dashed line for y = 3x, with the area below the line shaded.