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 linear equation as a dashed or solid line. Then, shade the region that satisfies the inequality (above for 'greater than' and below for 'less than').

Front

What does a dashed line indicate in graphing inequalities?

Back

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

Front

What does a solid line indicate in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (used for '≤' or '≥').

Front

What is the solution to the system of inequalities?

Back

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

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 point's coordinates into each inequality. If it satisfies all inequalities, it is a solution.

Front

What is the significance of the intersection of two lines in a system of equations?

Back

The intersection of two lines represents the solution to the system of equations, where both equations are satisfied.

Front

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

Back

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

Front

What does the inequality y ≥ -3/4x + 3 represent graphically?

Back

It represents the region above or on the line y = -3/4x + 3, including the line itself.

Front

How can you tell which side of the line to shade when graphing an inequality?

Back

You can test a point not on the line (like (0,0)). If it satisfies the inequality, shade the side containing that point.