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 points that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality on the same coordinate plane. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. The solution set is the overlapping shaded region.

Front

What does it mean if a system of equations has no solution?

Back

If a system of equations has no solution, it means that the lines representing the equations are parallel and will never intersect.

Front

What type of line is used to represent 'y < mx + b'?

Back

A dashed line is used to represent 'y < mx + b' because the inequality does not include the boundary line.

Front

What does the solution set of a system of inequalities represent?

Back

The solution set represents all the points (x, y) that satisfy all inequalities in the system.

Front

How can you determine if a point is part of the solution set for a system of inequalities?

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 difference between '≥' and '>' in inequalities?

Back

'≥' means 'greater than or equal to' and includes the boundary line, while '>' means 'greater than' and does not include the boundary line.

Front

What does the graph of 'x ≥ -3' look like?

Back

The graph of 'x ≥ -3' is a solid vertical line at x = -3, with shading to the right, indicating all values greater than or equal to -3.

Front

What is the significance of a solid line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is '≤' or '≥'.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is '<' or '>'.