System 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 ordered pairs 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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the symbol '≤' mean in an inequality?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean in an inequality?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane. The boundary line is dashed if the inequality is strict (< or >) and solid if it includes equality (≤ or ≥).

Front

How do you graph the inequality y < 2x - 4?

Back

1. Graph the line y = 2x - 4 as a dashed line. 2. Shade below the line to represent all points where y is less than 2x - 4.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap. It contains all points that satisfy all inequalities in the system.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it satisfies the equation of the line. Whether it is included in the solution set depends on the type of inequality (strict or non-strict).

Front

How can you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region. 3. The overlapping region represents the solution set.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' represents a strict inequality with a dashed line, while 'y ≤ mx + b' includes the line itself, represented by a solid line.