System of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A set of two or more linear inequalities that share the same variables.

Front

How do you graph a system of linear inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality. 4. The solution set is where the shaded regions overlap.

Front

What does it mean if a point is a solution to a system of inequalities?

Back

It means that the point satisfies all the inequalities in the system.

Front

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

Back

The boundary line represents the values where the inequality changes from true to false.

Front

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

Back

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

Front

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

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the solution set of a system of linear inequalities represent?

Back

It represents all the possible solutions that satisfy all inequalities in the system.

Front

What is the graphical representation of the inequality y < 2?

Back

A horizontal line at y = 2, shaded below the line.

Front

What is the graphical representation of the inequality y > 2x - 4?

Back

A dashed line for y = 2x - 4, shaded above the line.

Front

How do you find the intersection of two inequalities?

Back

Graph both inequalities and identify the region where the shaded areas overlap.