Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear 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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to that inequality, typically shaded on one side of the boundary line.

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 boundary line in a linear inequality?

Back

The boundary line represents the points where the inequality changes from true to false. It is solid for '≥' or '≤' and dashed for '>' or '<'.

Front

How do you graph a system of linear inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it is a solution if the inequality includes equality (≥ or ≤). If the inequality is strict (> or <), the point is not a solution.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap, representing all possible solutions.

Front

How can you tell if a point is not a solution to a system of inequalities?

Back

A point is not a solution if it does not satisfy at least one of the inequalities when substituted into them.

Front

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

Back

Test points are used to determine which side of the boundary line to shade. If the test point satisfies the inequality, shade the region containing that point.