Systems of Inequalities

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 graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution to the system is where the shaded regions overlap.

Front

What does the inequality 2x + 3y > 100 represent in a real-world context?

Back

It represents a situation where the total value of items (e.g., bracelets and earrings) sold must exceed $100.

Front

What does the inequality x + y ≤ 40 signify in a jewelry-making scenario?

Back

It signifies that the total number of pieces of jewelry (bracelets and earrings) made cannot exceed 40.

Front

What is the meaning of the symbol '≥' in inequalities?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to a specified number.

Front

What is the significance of the feasible region in a system of inequalities?

Back

The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions that satisfy 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 is the first step in solving a system of inequalities by graphing?

Back

The first step is to graph each inequality as if it were an equation, using a solid line for '≥' or '≤' and a dashed line for '>' or '<'.

Front

What does the inequality y < 2x - 4 represent graphically?

Back

It represents all points below the line y = 2x - 4 on a graph.

Front

In the context of baking cookies, what does the inequality 32x + 20y ≥ 150 mean?

Back

It means that the total number of cookies baked (32 chocolate chip cookies per hour and 20 snickerdoodle cookies per hour) must be at least 150.