Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

What does the symbol '≥' indicate in an inequality?

Back

'≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the number.

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 that points on the line are not included (> or <).

Front

How do you graph the inequality y < 2?

Back

Graph a horizontal line at y = 2, use a dashed line, and shade the area below the line.

Front

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

Back

The solution set represents all the points that satisfy all inequalities in the system simultaneously.

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 is the graphical representation of the system y > 2x - 4 and y < 2?

Back

Graph the line y = 2x - 4 with a dashed line and shade above it, then graph y = 2 with a dashed line and shade below it.

Front

What does it mean if a point lies in the shaded region of a graph of inequalities?

Back

It means that the point satisfies all the inequalities represented in the graph.

Front

How do you identify the correct graph for a given inequality?

Back

Analyze the inequality, determine the boundary line (solid or dashed), and identify the correct shading direction.

Front

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

Back

The solution is the region where both inequalities overlap, which can be found by graphing.