5.4 Solving Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

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

Front

How do you represent a solution to a system of linear inequalities on a graph?

Back

The solution is represented by the shaded region where all inequalities are satisfied, often bounded by solid or dotted lines.

Front

What does a dotted line indicate when graphing an inequality?

Back

A dotted line indicates that the points on the line are not included in the solution set, used for inequalities with < or >.

Front

What does a solid line indicate when graphing an inequality?

Back

A solid line indicates that the points on the line are included in the solution set, used for inequalities with ≤ or ≥.

Front

What is the graphical representation of the inequality 2x - y > 6?

Back

The graph will have a dotted line for the equation 2x - y = 6, and the solution will be the region above this line.

Front

How do you determine which region represents the solution to a system of inequalities?

Back

You test a point in each region to see if it satisfies all inequalities in the system.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of points that satisfy both inequalities, forming the solution region.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dotted line and does not include the line itself, while 'y ≤ mx + b' uses a solid line and includes the line.

Front

How do you graph the inequality y > 2x - 4?

Back

Graph the line y = 2x - 4 with a dotted line and shade above the line to represent y values greater than the line.

Front

What does the inequality x < -1 represent on a number line?

Back

It represents all numbers to the left of -1, not including -1 itself.