2.6 - 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 region where the graphs of the inequalities overlap.

Front

What does the slope-intercept form of a linear equation look like?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert an inequality to slope-intercept form?

Back

To convert an inequality to slope-intercept form, isolate y on one side of the inequality. For example, from ax + b < y, rearrange to y > ax + b.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. Shade the region that satisfies the inequality.

Front

What is the solution set of a system of inequalities?

Back

The solution set of a system of inequalities is the set of all points that satisfy all inequalities in the system, represented by the overlapping shaded regions on a graph.

Front

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

Back

To determine if a point is a solution, 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 y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis. It helps in graphing the inequality and understanding the relationship between variables.

Front

What is the slope in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).