Graphing Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

How do you rewrite a linear inequality in 'y=' form?

Back

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

Front

What does the solution of a system of linear inequalities represent?

Back

The solution of a system of linear inequalities represents all the points (x, y) that satisfy all inequalities in the system.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane, which is the area above or below the line defined by the corresponding linear equation.

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.

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What does it mean if a system of inequalities has no solution?

Back

A system of inequalities has no solution if the regions represented by the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

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What does it mean if a system of inequalities has infinitely many solutions?

Back

A system of inequalities has infinitely many solutions if the inequalities overlap in such a way that there are countless points that satisfy all of them.

Front

How do you graph a system of linear inequalities?

Back

To graph a system of linear inequalities, graph each inequality on the same coordinate plane, shading the appropriate half-plane for each, and identify the region where all shaded areas overlap.

Front

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

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not.