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

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 point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does a solid line represent in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does a dashed line represent in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is 'greater than' (>) or 'less than' (<).

Front

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

Back

The graph of y > -2x + 3 is a region above the line y = -2x + 3, with a dashed line.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the slope and y-intercept of the line, determine if the line is solid or dashed, and decide if the shaded region is above or below the line.

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

What does the solution set of a system of inequalities look like?

Back

The solution set is the overlapping region where all inequalities are satisfied, often represented as a shaded area on a graph.

Front

How can you graph the system of inequalities y < 3x + 1 and y ≥ -x - 2?

Back

Graph the line y = 3x + 1 with a dashed line and shade below it. Then graph y = -x - 2 with a solid line and shade above it. The solution is where the shaded areas overlap.

Front

What is the significance of the y-intercept in an inequality?

Back

The y-intercept is the point where the line crosses the y-axis, and it helps to determine the starting point for graphing the inequality.