Systems of Inequalities

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 find the perimeter of a rectangle?

Back

The perimeter of a rectangle is found using the formula P = 2(length + width).

Front

If the length of a rectangle is 3 times the width, how can you express the length in terms of the width?

Back

Length = 3 * Width.

Front

What is the formula for the area of a rectangle?

Back

Area = Length * Width.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution if it satisfies all inequalities in the system.

Front

How can you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, shading the region that satisfies each inequality.

Front

What is the significance of the boundary line in an inequality?

Back

The boundary line represents the points where the inequality changes from true to false. If the inequality is strict (>, <), the line is dashed; if it includes equality (≥, ≤), the line is solid.

Front

What does the notation y > 2x - 4 represent?

Back

It represents the region above the line y = 2x - 4, where y is greater than the value of 2x - 4.

Front

How do you determine if a point is a solution to the inequality y < 2?

Back

Substitute the x-value of the point into the inequality. If the resulting y-value is less than 2, then the point is a solution.

Front

What is the meaning of the inequality x + y ≤ 300 in a real-world context?

Back

It represents a constraint where the total number of adults (x) and children (y) cannot exceed 300 seats.