12-18-24 Systems of Inequalities Word Problems

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you represent a situation with a system of inequalities?

Back

You identify the variables, write inequalities based on the conditions given, and combine them to form a system.

Front

What does the symbol '≥' mean in inequalities?

Back

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

Front

What does the symbol '≤' mean in inequalities?

Back

'≤' means 'less than or equal to'. It indicates that the value can be either less than or equal to a certain number.

Front

How do you graph a system of inequalities?

Back

You graph each inequality on the same coordinate plane, using dashed lines for '<' or '>' and solid lines for '≤' or '≥'. The solution is the overlapping shaded region.

Front

What is the difference between a system of equations and a system of inequalities?

Back

Systems of equations have specific solutions (one, none, or infinite), while systems of inequalities can have a range of solutions represented by shaded regions.

Front

If x + y = 6, what does this represent?

Back

This represents a linear equation where the sum of x and y is equal to 6. It can be graphed as a straight line on a coordinate plane.

Front

In the context of inequalities, what does 'at least' mean?

Back

'At least' indicates a minimum value that must be met or exceeded, often represented by '≥'.

Front

In the context of inequalities, what does 'no more than' mean?

Back

'No more than' indicates a maximum value that cannot be exceeded, often represented by '≤'.

Front

How do you solve a word problem involving a system of inequalities?

Back

Identify the variables, translate the problem into inequalities, graph the inequalities, and find the overlapping solution region.