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

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'. It indicates that a value can be either greater than or equal to another value.

Front

What does the symbol '>' mean?

Back

'>' means 'greater than'. It indicates that a value is strictly greater than another value.

Front

How do you graph a linear inequality?

Back

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

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap. It represents all possible solutions that satisfy all inequalities.

Front

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

Back

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

Front

What is the difference between 'solution' and 'not a solution' in the context of inequalities?

Back

A 'solution' satisfies all inequalities in the system, while 'not a solution' does not satisfy at least one inequality.

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, it is a solution if the inequality includes '≥' or '≤'. If the inequality is '>' or '<', it is not a solution.

Front

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

Back

The shaded region represents all the possible solutions to the inequality. Points in this region satisfy the inequality.

Front

How do you identify the correct graph for a system of inequalities?

Back

Analyze the inequalities, determine the boundary lines, and check the shaded regions to see which graph represents the solution set.