Graphing Systems of 3 Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥) instead of an equal sign.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the region that satisfies the inequality.

Front

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

Back

The solution set of a system of inequalities represents all the points (x, y) that satisfy all the inequalities in the system simultaneously.

Front

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

Back

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

Front

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

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

Back

The intersection of shaded regions represents the solution set of the system of inequalities, where all conditions are satisfied.

Front

What does the notation 'y > mx + b' represent?

Back

The notation 'y > mx + b' represents a linear inequality where 'm' is the slope and 'b' is the y-intercept, indicating that y is greater than the value of the linear expression.

Front

How do you find the boundary line for a system of inequalities?

Back

To find the boundary line, convert the inequalities into equations by replacing the inequality sign with an equal sign, then graph the resulting linear equations.

Front

What is the role of the y-intercept in graphing linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis and is used to help graph the linear equation that forms the boundary of the inequality.

Front

What is a feasible region in the context of linear inequalities?

Back

A feasible region is the area on the graph that satisfies all inequalities in a system, representing all possible solutions.