2,9 systems of linear inequalities word problems

Front

What is a system of linear inequalities?

Back

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

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How do you represent a word problem as a system of inequalities?

Back

Identify the variables, determine the constraints (limits) and objectives, and translate them into inequalities based on the relationships described in the problem.

Front

What does the inequality x + y ≤ 6 represent in a word problem context?

Back

It indicates that the total number of items represented by x and y cannot exceed 6.

Front

What does the inequality 32x + 20y ≥ 150 represent in a word problem context?

Back

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

Front

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

Back

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

Front

What is the significance of the '≤' symbol in inequalities?

Back

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

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for '>' or '<' and a solid line for '≥' or '≤'. 3. Shade the region that satisfies the inequality.

Front

What does it mean if a point lies in the shaded region of a graph of a system of inequalities?

Back

It means that the point satisfies all inequalities in the system.

Front

What is the feasible region in the context of linear inequalities?

Back

The feasible region is the area on the graph where all the inequalities in the system overlap, representing all possible solutions.

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

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.