Solving Systems of Linear Inequalities

Front

What is a linear inequality?

Back

Front

How do you graph a linear inequality?

Back

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

Front

What does it mean for a point to be a solution of a system of linear inequalities?

Back

A point is a solution of a system of linear inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph for each inequality.

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 can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, 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 solution set of a system of linear inequalities?

Back

The solution set of a system of linear inequalities is the set of all points that satisfy all inequalities in the system, represented by the overlapping shaded regions on the graph.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left side of the inequality is either greater than or equal to the value on the right side.

Front

What does the symbol '<' mean in a linear inequality?

Back

The symbol '<' means 'less than', indicating that the value on the left side of the inequality is strictly less than the value on the right side.

Front

How do you write a system of linear inequalities from a graph?

Back

To write a system of linear inequalities from a graph, identify the lines and their slopes, then express each line as an inequality based on the shaded region.

Front

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

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The intersection of two shaded regions represents the set of solutions that satisfy both inequalities in the system.