System 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 a line is solid or dashed when graphing inequalities?

Back

A solid line is used when the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤). A dashed line is used when the inequality is 'greater than' (>) or 'less than' (<).

Front

What does it mean to shade above a line in a graph of an inequality?

Back

Shading above a line indicates that the solutions to the inequality are all the points where the y-value is greater than the value of the line at that x-value.

Front

What does it mean to shade below a line in a graph of an inequality?

Back

Shading below a line indicates that the solutions to the inequality are all the points where the y-value is less than the value of the line at that x-value.

Front

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

Back

To graph y > 2x - 4, first graph the line y = 2x - 4 using a dashed line, then shade above the line to represent all points where y is greater than 2x - 4.

Front

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

Back

The boundary line separates the coordinate plane into two regions, one where the inequality holds true and one where it does not. The line itself may or may not be included in the solution set, depending on whether it is solid or dashed.

Front

How can you determine the solution set of a system of inequalities graphically?

Back

To determine the solution set graphically, graph each inequality on the same coordinate plane, then identify the region where the shaded areas overlap. This overlapping region represents the solution set.

Front

What is the difference between 'y ≥ mx + b' and 'y > mx + b'?

Back

'y ≥ mx + b' includes the line itself (solid line), while 'y > mx + b' does not include the line (dashed line). The shading for 'y ≥' is above the line, and for 'y >', it is also above the line.

Front

What is the first step in solving a system of inequalities by graphing?

Back

The first step is to rewrite each inequality in slope-intercept form (y = mx + b) if necessary, to easily identify the slope and y-intercept for graphing.

Front

How do you identify the correct system of inequalities from a graph?

Back

To identify the correct system of inequalities from a graph, observe the boundary lines (solid or dashed) and the shaded regions. Write the inequalities based on the slopes and intercepts of the lines and the direction of the shading.