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 set of all points that satisfy all inequalities in the system.

Front

How do you determine if a point is a solution to a system of linear inequalities?

Back

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

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 linear inequalities?

Back

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

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

How can you graph a system of linear inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a solid or dashed line as appropriate. 3. Shade the appropriate region for each inequality. 4. Identify the overlapping shaded region.

Front

What does it mean for a point to be 'not part of the solution set'?

Back

A point is 'not part of the solution set' if it does not satisfy at least one of the inequalities in the system.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the graph into two half-planes, one representing solutions that satisfy the inequality and the other representing those that do not.

Front

How do you solve a system of linear inequalities by graphing?

Back

1. Graph each inequality. 2. Identify the feasible region where all inequalities overlap. 3. The overlapping region is the solution set.

Front

What is an example of a solution to a system of linear inequalities?

Back

For the inequalities y > 2x + 1 and y < -x + 4, the point (1, 3) is a solution because it satisfies both inequalities.