Solving 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 region where the graphs of the inequalities overlap.

Front

What does the symbol '>' represent in an inequality?

Back

The symbol '>' 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 an inequality?

Back

The symbol '<' 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 an inequality?

Back

The symbol '≥' 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 an inequality?

Back

The symbol '≤' 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 graph the inequality y > x + 1?

Back

To graph y > x + 1, first graph the line y = x + 1 as a dashed line (since it's a 'greater than' inequality). Then shade the region above the line.

Front

How do you graph the inequality y ≤ -x + 1?

Back

To graph y ≤ -x + 1, first graph the line y = -x + 1 as a solid line (since it's a 'less than or equal to' inequality). Then shade the region below the line.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (for ≤ or ≥). A dashed line indicates that the points on the line are not included (for < or >).

Front

What is the solution to the system of inequalities: y > 2x - 4 and y < 2?

Back

The solution is the region where the graph of y > 2x - 4 overlaps with the graph of y < 2.

Front

How do you write the inequality for the shaded region above the line y = -2?

Back

The inequality for the shaded region above the line y = -2 is y > -2.