Systems 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 region where the graphs of the inequalities overlap.

Front

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, which occurs when the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, which occurs when the inequality is 'greater than' (>) or 'less than' (<).

Front

How do you determine which direction to shade when graphing an inequality?

Back

If the inequality symbol is 'greater than' (>) or 'greater than or equal to' (≥), shade above the line. If it is 'less than' (<) or 'less than or equal to' (≤), shade below the line.

Front

What is the solution to the system of inequalities: y < 2x + 3 and y > -x + 1?

Back

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

Front

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

Back

It means that the graphs of the inequalities do not intersect, and there is no set of values that satisfies all inequalities simultaneously.

Front

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

Back

It means that there are an unlimited number of points that satisfy all inequalities, often occurring when the inequalities represent the same line.

Front

How do you graph the inequality y ≤ 2x - 1?

Back

Graph the line y = 2x - 1 with a solid line, then shade below the line to indicate all points where y is less than or equal to 2x - 1.

Front

What is the significance of the intersection point in a system of inequalities?

Back

The intersection point represents a solution that satisfies all inequalities in the system.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the shaded regions. 3. The solution is where the shaded regions overlap.