Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

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

Back

It means that there is no set of values for the variables that can satisfy all inequalities simultaneously.

Front

What does it mean if a system of inequalities has an infinite number of solutions?

Back

It means that there are countless combinations of values for the variables that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane, using dashed lines for < or > and solid lines for ≤ or ≥. The solution is the overlapping shaded region.

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

What is the solution set of the inequalities y < 2x + 3 and y ≥ -x - 1?

Back

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

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 does the inequality y > -x - 1 represent graphically?

Back

It represents the region above the line y = -x - 1, not including the line itself.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line helps to define the regions of solutions. It separates the area where the inequalities are satisfied from where they are not.

Front

What is the graphical representation of the inequality 2x - y > 4?

Back

The graph will have a dashed line for the equation 2x - y = 4, and the solution will be the area above this line.