System of Inequalities

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 system of inequalities?

Back

To graph a system of inequalities, first graph each inequality on the same coordinate plane. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. Shade the appropriate region that satisfies each inequality.

Front

What does a solid line indicate in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, which is the case for inequalities like '≥' or '≤'.

Front

What does a dashed line indicate in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, which is the case for inequalities like '>' or '<'.

Front

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

Back

A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities simultaneously.

Front

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

Back

A system of inequalities has infinite solutions if the shaded regions overlap completely, meaning there are infinitely many points that satisfy all inequalities.

Front

How do you determine which region to shade for the inequality y ≥ mx + b?

Back

For the inequality y ≥ mx + b, shade above the line because it includes all points where y is greater than or equal to the value of mx + b.

Front

How do you determine which region to shade for the inequality y < mx + b?

Back

For the inequality y < mx + b, shade below the line because it includes all points where y is less than the value of mx + b.

Front

What is the significance of the slope in a linear inequality?

Back

The slope (m) in a linear inequality indicates the steepness and direction of the line. A positive slope rises from left to right, while a negative slope falls from left to right.

Front

What is the y-intercept in a linear inequality?

Back

The y-intercept (b) in a linear inequality is the point where the line crosses the y-axis, representing the value of y when x = 0.