4.5 Systems of Inequalities

Front

What is a system of inequalities?

Back

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

Front

How do you determine if an ordered pair is a solution to a system of inequalities?

Back

To determine if an ordered pair is a solution, substitute the values of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, typically shown as a shaded region on one side of the boundary line.

Front

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

Back

'y < mx + b' indicates that the line is not included in the solution (dashed line), while 'y ≤ mx + b' includes the line (solid line) in the solution.

Front

What does it mean to graph a system of inequalities?

Back

Graphing a system of inequalities involves plotting each inequality on the same coordinate plane and identifying the region where all shaded areas overlap, which represents the solution set.

Front

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

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not. The line itself may or may not be included in the solution.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. 3. Shade the appropriate region for each inequality. 4. Identify the overlapping shaded region as the solution.

Front

What is the solution to the system of inequalities y < -x + 2 and y > 3?

Back

The solution is the region above the line y = -x + 2 and below the line y = 3, where the two regions overlap.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it is included in the solution if the inequality is '≤' or '≥', but not included if the inequality is '<' or '>'.

Front

What is the graphical representation of the inequality y ≥ -2x + 3?

Back

The graphical representation includes a solid line for y = -2x + 3 and the region above the line, indicating all points where y is greater than or equal to -2x + 3.