Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

What does the symbol '>' indicate in an inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

What does the symbol '<' indicate in an inequality?

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

When do you use a solid line when graphing inequalities?

Back

A solid line is used when graphing inequalities with the symbols ≤ (less than or equal to) or ≥ (greater than or equal to).

Front

When do you use a dotted line when graphing inequalities?

Back

A dotted line is used when graphing inequalities with the symbols < (less than) or > (greater than).

Front

What is the solution set of a system of inequalities?

Back

The solution set of a system of inequalities is the set of all points that satisfy all inequalities in the system.

Front

How do you determine if a point is part of the solution set?

Back

To determine if a point is part of the solution set, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

What is the graphical representation of the inequality y < 2?

Back

The graphical representation of the inequality y < 2 is a horizontal line at y = 2 with a dotted line, shading the area below the line.

Front

What is the graphical representation of the inequality y > 2x - 4?

Back

The graphical representation of the inequality y > 2x - 4 is a straight line with a slope of 2 and a y-intercept of -4, using a dotted line, shading the area above the line.

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 of an inequality, it is part of the solution set only if the inequality includes equality (≤ or ≥).