MW Systems 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

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system when substituted into them.

Front

How do you determine if a point is a solution to a given inequality?

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a line. The line represents the boundary, and the shaded area indicates the solutions.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating 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

The symbol '>' means 'greater than', indicating that the value on the left must be strictly greater than the value on the right.

Front

What is the difference between 'no solution' and 'infinite solutions' in a system of inequalities?

Back

'No solution' means there are no points that satisfy all inequalities, while 'infinite solutions' means there are countless points that satisfy all inequalities.

Front

How can you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality as a line, shade the appropriate half-plane for each, and identify the region where the shaded areas overlap.

Front

What is a boundary line in the context of inequalities?

Back

A boundary line is the line that represents the equation of the inequality. It divides the coordinate plane into two regions.

Front

What does it mean if a boundary line is dashed?

Back

A dashed boundary line indicates that points on the line are not included in the solution set (for inequalities using '<' or '>').