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 shaded areas of the inequalities overlap.

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 is the difference between a system of equations and a system of inequalities?

Back

Systems of equations have specific solutions (one, none, or infinitely many), while systems of inequalities represent a range of solutions, often visualized as shaded regions on a graph.

Front

What does it mean to graph a system of inequalities?

Back

Graphing a system of inequalities involves drawing the lines of the inequalities and shading the appropriate regions to represent all possible solutions.

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

How do you graph the inequality y > 2x + 1?

Back

Graph the line y = 2x + 1 as a dashed line (since it's >, not ≥) and shade above the line to represent all points where y is greater than 2x + 1.

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set (for inequalities like < or >).

Front

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (for inequalities like ≤ or ≥).

Front

How can you find the solution to a system of inequalities graphically?

Back

To find the solution graphically, graph each inequality, shade the appropriate regions, and identify the overlapping shaded area, which represents the solution.

Front

What is the solution set of the system of inequalities x + y < 5 and x - y > 1?

Back

The solution set is the region where the shaded areas of both inequalities overlap on the graph.