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 word problem as a system of inequalities?

Back

Identify the variables, write inequalities based on the conditions given in the problem, and ensure they reflect the relationships described.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane. Use a dashed line for '>' or '<' and a solid line 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 Eiko can complete a small drawing in 15 minutes, how many small drawings can she complete in 480 minutes?

Back

Eiko can complete 32 small drawings in 480 minutes (480 ÷ 15 = 32).

Front

If Eiko wants to make at least $200, how can we express this as an inequality?

Back

Let x be the number of small drawings and y be the number of large drawings. The inequality is 10x + 25y ≥ 200.

Front

What does it mean if a student has 'less than 180 days left of school'?

Back

This can be expressed as an inequality: x < 180, where x represents the number of days left.

Front

How do you determine if a solution satisfies a system of inequalities?

Back

Substitute the values into each inequality. If all inequalities are true, the solution satisfies the system.