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 the graph of an inequality represent?

Back

The graph of an inequality represents all the solutions to that inequality, typically shaded to show the region that satisfies the inequality.

Front

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

Back

'>' means greater than and does not include the boundary line, while '≥' means greater than or equal to and includes the boundary line.

Front

What does 'y < 2x - 4' represent graphically?

Back

It represents the region below the line y = 2x - 4, where all points (x, y) satisfy the inequality.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, shading the appropriate region for each. The solution is where the shaded regions overlap.

Front

What is the significance of the boundary line in an inequality?

Back

The boundary line represents the points where the inequality changes from true to false. It is included in the solution if the inequality is '≤' or '≥'.

Front

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

Back

The solution set is typically a shaded region on a graph, representing all the points that satisfy all inequalities in the system.

Front

How can you check if a point is a solution to a system of inequalities?

Back

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

Front

What is the role of test points in solving systems of inequalities?

Back

Test points are used to determine which regions of the graph satisfy the inequalities. If a test point in a region satisfies all inequalities, that region is part of the solution.