2.7 Writing Linear Inequalities in Two Variables

Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be expressed in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants and x and y are variables.

Front

How do you represent a situation where a total must exceed a certain amount using a linear inequality?

Back

You can represent this situation by using the inequality symbol '>' to indicate that the total must be greater than the specified amount.

Front

What does the inequality 2x + 0.75y > 180 represent in a real-world context?

Back

This inequality represents a scenario where the total revenue from selling x hot dogs at $2 each and y sodas at $0.75 each must exceed $180.

Front

How do you write an inequality for a budget constraint?

Back

You write an inequality using the '≤' symbol to indicate that the total cost must not exceed the budget.

Front

What is the significance of the coefficients in a linear inequality?

Back

The coefficients represent the rate of change or contribution of each variable to the total value being considered in the inequality.

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How can you determine the feasible region for a system of linear inequalities?

Back

The feasible region can be determined by graphing the inequalities on a coordinate plane and identifying the area where all inequalities overlap.

Front

What does the inequality 200x + 250y ≥ 3200 indicate about ticket sales?

Back

This inequality indicates that the total revenue from selling x adult tickets at a price of x and y child tickets at a price of y must be at least $3200.

Front

How do you solve a linear inequality involving two variables?

Back

To solve a linear inequality involving two variables, you can graph the corresponding equation and then determine which side of the line satisfies the inequality.

Front

What is the difference between '>' and '≥' in linear inequalities?

Back

The symbol '>' indicates that the value must be strictly greater than, while '≥' indicates that the value can be equal to or greater than.

Front

How do you interpret the solution of a linear inequality?

Back

The solution of a linear inequality represents all the possible values of the variables that satisfy the inequality.