Solving Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear 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

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.

Front

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

Back

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

Front

What does the symbol '<' mean in an inequality?

Back

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

Front

What does the symbol '≥' mean in an inequality?

Back

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

Front

What does the symbol '≤' mean in an inequality?

Back

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

Front

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

Back

The solution is the region above the line y = 2x - 4, not including the line itself.

Front

What is the solution to the inequality y ≤ -x + 1?

Back

The solution is the region below the line y = -x + 1, including the line itself.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

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

Back

The shaded region represents all the possible solutions to the system of inequalities.