Systems of Linear Inequalities from a Graph

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution if it lies in the region where all inequalities overlap on a graph.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a line. The line represents the boundary, and the shaded area indicates the solutions.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you graph a system of linear inequalities?

Back

1. Graph each inequality as a line. 2. Use solid or dashed lines as appropriate. 3. Shade the appropriate half-plane for each inequality. 4. The solution is where the shaded regions overlap.

Front

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

Back

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

Front

Can a system of linear inequalities have no solution?

Back

Yes, a system can have no solution if the inequalities represent parallel lines that do not intersect.

Front

What is an ordered pair in the context of linear inequalities?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on the Cartesian plane.

Front

How can you check if an ordered pair is a solution to a system of inequalities?

Back

Substitute the x and y values of the ordered pair into each inequality. If all inequalities are satisfied, it is a solution.