Practice Graphing System 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 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 '>'. Then shade the region that satisfies the inequality.

Front

What does it mean if a point is a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

What does the shaded area represent in the graph of an inequality?

Back

The shaded area represents all the possible solutions to the inequality, indicating where the inequality holds true.

Front

How can you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set for the inequality.

Front

What does the inequality y < 2x + 3 represent graphically?

Back

It represents all the points below the line y = 2x + 3, which is graphed with a dashed line.

Front

What is the solution set of the inequality y ≥ -x + 1?

Back

The solution set includes all points on and above the line y = -x + 1, which is graphed with a solid line.

Front

How do you identify a point that is not a solution to a system of inequalities?

Back

A point that is not a solution will not satisfy at least one of the inequalities in the system when substituted into them.