5.4 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 that involve 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 (depending on whether the inequality is strict or inclusive). Then, shade the region that satisfies the inequality.

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What does the symbol '>' mean 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 '<' mean 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 '≥' mean 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 '≤' mean 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 can you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, 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 the graph of a system of inequalities?

Back

The shaded region represents all possible solutions to the system of inequalities. Any point within this region satisfies all inequalities in the system.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (using '>' or '<') does not include the boundary line, while a non-strict inequality (using '≥' or '≤') includes the boundary line.

Front

How do you solve a system of linear inequalities graphically?

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To solve graphically, graph each inequality on the same coordinate plane, identify the shaded regions, and find the intersection of these regions, which represents the solution set.