Solutions to Systems of Inequalities- Graphs!

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 ordered pairs 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 as if it were an equation. Then, determine the solution region by shading the area that satisfies all inequalities.

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 inequalities in the system when the coordinates of the point are substituted into the inequalities.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

Front

What is the solution region in a graph of inequalities?

Back

The solution region is the area on the graph where all the inequalities in the system overlap, representing all possible solutions.

Front

How do you determine if a point is in the solution region?

Back

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

Front

What does the term 'ordered pair' mean?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, written in the form (x, y).

Front

What is the significance of the boundary line in a graph of inequalities?

Back

The boundary line represents the points where the inequality changes from true to false. For strict inequalities, the line is dashed; for non-strict inequalities, it is solid.

Front

How can you tell if a point is a solution to a specific inequality?

Back

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

Front

What does it mean if a solution is 'not a solution' to a system of inequalities?

Back

If a point is 'not a solution,' it means that when the coordinates are substituted into the inequalities, at least one inequality is not satisfied.