Systems of Inequalities: Graphing and Solutions

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

Front

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

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

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

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

How can you determine if an ordered pair is a solution to an inequality?

Back

To determine if an ordered pair is a solution to an inequality, substitute the x and y values of the pair into the inequality. If the inequality holds true, then the ordered pair is a solution.

Front

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

Back

The boundary line represents the values that make the inequality an equation. If the inequality is strict (>, <), the line is dashed; if it is inclusive (≥, ≤), the line is solid.

Front

What is the solution set of a system of inequalities?

Back

The solution set of a system of inequalities is the region where the shaded areas of all inequalities overlap on the graph.

Front

How do you find the intersection of two inequalities?

Back

To find the intersection of two inequalities, graph both inequalities on the same coordinate plane and identify the region where the shaded areas overlap.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert an inequality to slope-intercept form?

Back

To convert an inequality to slope-intercept form, isolate y on one side of the inequality, resulting in the form y < mx + b or y > mx + b.