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 graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality on the same coordinate plane. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. Shade the appropriate region for each inequality.

Front

What does it mean for a point to be 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 is the significance of the shaded region in the graph of inequalities?

Back

The shaded region represents all possible solutions to the inequality. Any point within this region satisfies the inequality.

Front

How can 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 the inequality y < -x - 1 represent graphically?

Back

It represents all points below the line y = -x - 1, which has a slope of -1 and a y-intercept of -1.

Front

What does the inequality y ≥ x + 4 represent graphically?

Back

It represents all points on or above the line y = x + 4, which has a slope of 1 and a y-intercept of 4.

Front

What is the solution set of the system: y < -x - 1 and y ≥ x + 4?

Back

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

Front

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

Back

To identify the correct graph, analyze the inequalities, determine the lines and shading, and compare with the provided options.