System of Linear Inequalities Practice

Front

What is a system of linear inequalities?

Back

A set of two or more linear inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

What does the symbol '>' represent in inequalities?

Back

It indicates that the value on the left is greater than the value on the right.

Front

What does the symbol '≥' represent in inequalities?

Back

It indicates that the value on the left is greater than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. 3. Shade the region that satisfies the inequality.

Front

What is the solution set of a system of inequalities?

Back

The set of all points that satisfy all inequalities in the system.

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What does it mean if a system of inequalities has no solution?

Back

It means that there is no point that satisfies all inequalities in the system, often represented by parallel lines.

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What does it mean if a system of inequalities has infinitely many solutions?

Back

It means that there are an infinite number of points that satisfy all inequalities, often represented by overlapping lines.

Front

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

Back

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

Front

What is the difference between '>' and '≥' in terms of solutions?

Back

'>' does not include the boundary line in the solution set, while '≥' includes it.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all possible solutions to the inequality.