Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear 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

How do you determine if a line is solid or dashed in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

Front

What does the inequality y ≤ 2x - 1 represent graphically?

Back

It represents all the points on or below the line y = 2x - 1.

Front

What is the solution to the inequality 5 ≥ x?

Back

The solution is all values of x that are less than or equal to 5.

Front

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

Back

Graph the line y = -2x + 3 with a dashed line and shade above the line.

Front

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

Back

A point is a solution if it satisfies all inequalities in the system.

Front

How can you check if a point (2, -5) is a solution to the system of inequalities?

Back

Substitute x = 2 and y = -5 into each inequality. If all inequalities are satisfied, then (2, -5) is a solution.

Front

What is the significance of the intersection of the shaded regions in a graph of inequalities?

Back

The intersection represents the set of all solutions that satisfy all inequalities in the system.

Front

What is the graphical representation of the inequality y < 2x - 1?

Back

It is represented by a dashed line for y = 2x - 1, with shading below the line.

Front

What does the term 'feasible region' refer to in linear inequalities?

Back

The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions.