Systems of Inequalities: Graphing and Solutions

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 linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. Then shade the appropriate region based on the inequality.

Front

What does it mean to shade above a line in a graph?

Back

Shading above a line indicates that the solutions to the inequality are all the points above the line, meaning the y-values are greater than the values on the line.

Front

What does it mean to shade below a line in a graph?

Back

Shading below a line indicates that the solutions to the inequality are all the points below the line, meaning the y-values are less than the values on the line.

Front

What is the solution to a system of inequalities?

Back

The solution to a system of inequalities is the region where the shaded areas of all inequalities overlap on the graph.

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 x and y values 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 values where the inequality changes from true to false. Points on the line may or may not be included in the solution set, depending on whether the inequality is strict or inclusive.

Front

What does the inequality y ≤ 2/5x + 1 represent graphically?

Back

It represents all points on or below the line y = 2/5x + 1, including the line itself.

Front

What is the difference between '>' and '≥' in inequalities?

Back

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

Front

How can you identify the solution to a system of equations graphically?

Back

The solution to a system of equations can be identified as the point where the graphs of the equations intersect.