Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A set of two or more linear inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

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

Back

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

Front

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

Back

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

Front

What is the solution set of a system of inequalities?

Back

The set of all points that satisfy all inequalities in the system, represented graphically as a shaded region.

Front

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

Back

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

Front

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

Back

The boundary line separates the solution region from the non-solution region. Points on the line are included if the inequality is ≤ or ≥.

Front

What does it mean if a system of inequalities has no solution?

Back

It means that there is no region where the graphs of the inequalities overlap; the inequalities contradict each other.

Front

What is the graphical representation of 'y < 2x - 4'?

Back

A dashed line representing the equation y = 2x - 4, with the area below the line shaded.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region as the solution set.