Systems of Inequalities Review

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 the solution set of a system of inequalities represent?

Back

The solution set represents all the points (x, y) that satisfy all inequalities in the system, often shown as a shaded region on a 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

If a system of inequalities has no solution, what does that mean?

Back

It means that there are no points that satisfy all inequalities in the system, often because the shaded regions do not overlap.

Front

What is the graphical representation of the inequality y < 3x?

Back

The graph is a dashed line with a slope of 3, and the area below the line is shaded.

Front

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

Back

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

Front

What does the inequality 8x + 25y ≥ 100 represent in a real-world context?

Back

It represents a constraint where the total earnings from two jobs must be at least $100.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.

Front

How can you tell if a point lies above or below a line in a graph?

Back

If the y-coordinate of the point is greater than the y-value of the line at the same x-coordinate, the point is above the line; if it is less, the point is below.