Unit 2 Review - 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 point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to that inequality, typically shown as a shaded region on one side of the boundary line.

Front

What is the difference between a solid line and a dashed line in the graph of inequalities?

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 - 4 represent graphically?

Back

It represents the region above the line y = 2x - 4, not including the line itself.

Front

How do you graph the inequality y ≤ 2/5x + 1?

Back

Graph the line y = 2/5x + 1 using a solid line, then shade below the line to represent all points where y is less than or equal to the line.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region where the shaded areas of all inequalities overlap on the graph.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it may or may not be a solution, depending on whether the inequality is strict (>) or inclusive (≥).

Front

How can you tell if a point is a solution to the inequality y < -x + 1?

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of points that satisfy both inequalities simultaneously, forming the solution to the system.