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 a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. Then shade the region that satisfies the inequality.

Front

What does the dashed line indicate in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is strict (e.g., '<' or '>').

Front

What does the solid line indicate in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is non-strict (e.g., '≤' or '≥').

Front

What is the solution to the system of inequalities: y < 2x + 1 and y > -x - 2?

Back

The solution is the region where the graphs of the inequalities overlap.

Front

What does it mean if a system of inequalities has no solution?

Back

It means that there is no set of values that satisfies all inequalities in the system, often because the lines representing the inequalities are parallel.

Front

What does it mean if a system of inequalities has infinite solutions?

Back

It means that there are countless pairs of values that satisfy all inequalities in the system, often because the lines overlap completely.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the y-intercept in the inequality y < mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, and it helps in graphing the inequality.

Front

What is the slope in the inequality y < mx + b?

Back

The slope (m) indicates the steepness of the line and the direction it goes (upward or downward) as x increases.