QTR 2: ALG U4 CW#2: Solving 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 that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

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

Back

The symbol '≤' 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 '≥' represent in an inequality?

Back

The symbol '≥' 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

When graphing the inequality y < 2x - 1, what type of line is used?

Back

A dotted line is used when graphing the inequality y < 2x - 1 because the inequality does not include equality.

Front

When graphing the inequality y ≥ -2x + 3, what type of line is used?

Back

A solid line is used when graphing the inequality y ≥ -2x + 3 because the inequality includes equality.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.

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

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 included in the solution set if the inequality is '≤' or '≥', but not if it is '<' or '>'.

Front

What is the graphical representation of the inequality y > x + 1?

Back

The graphical representation of y > x + 1 is a region above the line y = x + 1, using a dotted line for the boundary.

Front

What is the difference between a solid line and a dotted line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (for '≤' or '≥'), while a dotted line indicates that points on the line are not included (for '<' or '>').