Solving 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

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the region that satisfies the inequality.

Front

What does the symbol '≥' mean 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 does the symbol '≤' mean in an inequality?

Back

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

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.

Front

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

Back

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

Front

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

Back

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

Front

What does the inequality 'y < 2x + 3' represent graphically?

Back

It represents all points below the line y = 2x + 3, not including the line itself.

Front

How can you solve a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane and identify the overlapping shaded region as the solution.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of points that satisfy both inequalities simultaneously.