Solutions to Systems of Inequalities- Graphs!

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 graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation (using a solid line for '≤' or '≥' and a dashed line for '<' or '>'). 2. Shade the region that satisfies the inequality. 3. The solution to the system is where the shaded regions overlap.

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 satisfies all inequalities in the system, meaning it lies in the overlapping shaded region of the graph.

Front

What is the difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) means the value is strictly above, while 'greater than or equal to' (≥) includes the boundary value.

Front

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

Back

The boundary line represents the points where the inequality changes from true to false. It divides the graph into regions that satisfy or do not satisfy the inequality.

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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.

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What does the shaded region in a graph of inequalities represent?

Back

The shaded region represents all the possible solutions that satisfy the inequality.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the collection of all points that satisfy all inequalities in the system, often represented graphically.

Front

What is the role of the x and y axes in graphing inequalities?

Back

The x and y axes provide a coordinate system to plot points and graph inequalities, helping visualize the solution set.

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 included in the solution set if the inequality is '≤' or '≥', but not if it is '<' or '>'.