System 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 ordered pairs 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 the line for 'greater than' and below for 'less than').

Front

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 greater 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 less 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 feasible region in a system of inequalities?

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The feasible region is the area on the graph where all the shaded regions of the inequalities overlap. It represents all possible solutions to the system.

Front

How do you solve a system of inequalities algebraically?

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To solve a system of inequalities algebraically, isolate one variable in one inequality and substitute it into the other inequality, then solve for the remaining variable.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the values where the inequality changes from true to false. If the inequality is strict ('<' or '>'), the line is dashed; if it includes equality ('≤' or '≥'), the line is solid.