Systems of Inequalities Pre-Formative

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

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

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the inequality symbol '>' mean?

Back

'>' means that the value on the left is greater than the value on the right.

Front

What does the inequality symbol '<' mean?

Back

'<'' means that the value on the left is less than the value on the right.

Front

What does the inequality symbol '≥' mean?

Back

'≥' means that the value on the left is greater than or equal to the value on the right.

Front

What does the inequality symbol '≤' mean?

Back

'≤' means that the value on the left is less than or equal to the value on the right.

Front

How can you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Then, use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. Shade the region that satisfies the inequality.

Front

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

Back

The shaded region represents all the possible solutions to the system of inequalities.

Front

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

Back

Identify the variables, write inequalities based on the problem's conditions, and then solve the system to find the feasible solutions.

Front

What is the first step in solving the problem: JoAnn can work a maximum of 15 hours per week and wants to earn at least $66?

Back

Define the variables: let b = hours babysitting and t = hours tutoring. Write the inequalities: b + t < 15 and 3b + 6t > 66.