Systems of Inequalities (SOI)

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 it mean if an inequality is represented by a dashed line?

Back

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

Front

What does it mean if an inequality is represented by a solid line?

Back

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

Front

How do you graph the inequality y < 2x + 3?

Back

1. Graph the line y = 2x + 3 with a dashed line. 2. Shade the area below the line to represent y values that are less than 2x + 3.

Front

What is the solution to the system of inequalities x > 2 and y < -4?

Back

The solution is the region in the coordinate plane where x is greater than 2 and y is less than -4.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the solution region from the non-solution region. It helps to determine where the inequalities hold true.

Front

What does the term 'feasible region' refer to in the context of systems of inequalities?

Back

The feasible region is the area on the graph where all the inequalities in the system are satisfied.

Front

How can 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 graphical representation of the inequality y ≥ 3?

Back

Graph the line y = 3 with a solid line and shade the area above the line.

Front

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

Back

An inconsistent system has no solution; the graphs of the inequalities do not overlap.