Solving Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.

Front

How do you determine if an ordered pair is a solution to a system of inequalities?

Back

To determine if an ordered pair is a solution, substitute the values of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

Front

What does it mean to graph a system of inequalities?

Back

Graphing a system of inequalities involves plotting each inequality on the same coordinate plane and identifying the region where all inequalities overlap, which represents the solution set.

Front

How do you rewrite an inequality in 'y=' form?

Back

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

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line represents the equality part of the inequality. If the inequality is strict (>, <), the line is dashed; if it is inclusive (≥, ≤), the line is solid.

Front

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

Back

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

Front

How can you find the solution set of a system of inequalities graphically?

Back

To find the solution set graphically, graph each inequality, shade the appropriate regions, and identify the overlapping shaded area, which represents the solution set.

Front

What is the role of test points in solving systems of inequalities?

Back

Test points are used to determine which side of the boundary line satisfies the inequality. By substituting a test point into the inequality, you can see if it holds true.

Front

How do you solve a system of inequalities algebraically?

Back

To solve algebraically, you can isolate one variable in one inequality and substitute it into the other inequality, then solve for the variables.

Front

What is the graphical representation of the solution to the system of inequalities x + 2y ≥ 4 and 3x − 2y < 4?

Back

The solution is represented by the region where the shaded areas of both inequalities overlap on the graph.