Graphing systems 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 on the same coordinate plane. 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 it mean if a point is a solution to a system of inequalities?

Back

The point satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line represents the values where the inequality changes from true to false. Points on the line are included if the inequality is ≤ or ≥.

Front

What does the inequality y > 2x - 4 represent graphically?

Back

It represents the region above the line y = 2x - 4, not including the line itself.

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 does the inequality y ≤ x - 3 indicate about the graph?

Back

It indicates that the region below the line y = x - 3, including the line itself, is shaded.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) do include the boundary line.

Front

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

Back

An inconsistent system has no solution, meaning the shaded regions do not overlap.

Front

How can you identify a solution set from a graph of inequalities?

Back

The solution set is represented by the overlapping shaded regions of the graphed inequalities.