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

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. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.

Front

What does the symbol '>' represent in inequalities?

Back

'>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' represent in inequalities?

Back

'<'' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What does the symbol '≥' represent in inequalities?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

Front

What does the symbol '≤' represent in inequalities?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

Front

How do you convert an inequality to 'y=' form?

Back

To convert an inequality to 'y=' form, isolate y on one side of the inequality. For example, from 3x - 6y > 12, you would rearrange to y < (1/2)x - 2.

Front

What is the solution to the inequality y > 2x - 4 and y < 2?

Back

The solution is the region above the line y = 2x - 4 and below the line y = 2 on a graph.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all the possible solutions that satisfy the inequality or system of inequalities.

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.