Solving Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are solved together.

Front

What does the symbol '≤' mean?

Back

It means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

It means 'greater than or equal to'.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line as if it were an equation. 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 to a system of inequalities?

Back

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

Front

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

Back

It means there is no set of values that satisfies all inequalities simultaneously.

Front

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

Back

It represents all possible solutions to the inequality.

Front

What does it mean if two inequalities intersect on a graph?

Back

It indicates that there are common solutions that satisfy both inequalities.

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, it is a solution.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.