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 set of all points that satisfy all inequalities in the system.

Front

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

Back

It means that there is no point that satisfies all inequalities in the system, often because the lines representing the inequalities are parallel.

Front

What does it mean if a system of linear inequalities has an infinite number of solutions?

Back

It means that there are infinitely many points that satisfy all inequalities, typically when the inequalities represent the same line or overlapping regions.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

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

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the points where the inequality changes from true to false. It is included in the solution if the inequality is ≤ or ≥, and not included if it is < or >.

Front

What type of line is used when graphing y < mx + b?

Back

A dotted line is used to indicate that points on the line are not included in the solution.

Front

What does the symbol '≥' indicate in a linear inequality?

Back

It indicates that the values on the left side of the inequality are greater than or equal to the values on the right side.

Front

How do you graph the inequality y ≥ 2x + 1?

Back

Graph the line y = 2x + 1 with a solid line, then shade above the line to represent all points where y is greater than or equal to 2x + 1.

Front

What is the solution set of the inequalities y < 3 and y > -1?

Back

The solution set includes all points between the lines y = 3 and y = -1, not including the lines themselves.

Front

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

Back

'y ≤ mx + b' includes the boundary line (solid line), while 'y < mx + b' does not include the boundary line (dotted line).