4.6 Systems of Linear Inequalities

Front

What is a linear inequality?

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Front

How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it lies in the shaded region of the graph representing all inequalities in the system.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

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

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the solution set of a system of linear inequalities?

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The solution set is the region on the graph where the shaded areas of all inequalities overlap, representing all possible solutions.

Front

What is the graphical representation of the inequality @@y ge rac{3}{4}x - 2@@?

Back

Front

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Front

How do you solve a system of equations graphically?

Back

To solve a system of equations graphically, plot both equations on the same graph and identify the point(s) where the lines intersect. This point(s) is the solution.

Front

What is the significance of the intersection point in a system of linear equations?

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The intersection point represents the values of the variables that satisfy both equations simultaneously.