System 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.

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

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What does the graph of a linear inequality represent?

Back

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

Front

What is the difference between a solid line and a dashed line in the graph of 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

What does the inequality 2x - y > 4 represent graphically?

Back

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

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How do you graph a system of inequalities?

Back

1. Graph each inequality as a line (solid or dashed). 2. Shade the appropriate region for each inequality. 3. The solution is where the shaded regions overlap.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the set of all points that satisfy all inequalities in the system, represented graphically as the overlapping shaded region.

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What does the notation (x, y) mean in the context of inequalities?

Back

The notation (x, y) represents an ordered pair, where x is the value on the horizontal axis and y is the value on the vertical axis.

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 true, then the ordered pair is a solution.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the graph into two regions, indicating where the solutions to the inequalities lie.