Solving Systems 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 points that satisfy all inequalities in the system.

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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 does it mean for a point to be a solution of an inequality?

Back

A point is a solution of an inequality if it makes the inequality true when the coordinates of the point are substituted into the inequality.

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What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a boundary line. The line is solid if the inequality is inclusive (≥ or ≤) and dashed if it is exclusive (> or <).

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap. This overlapping region represents the solution set.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

Rewrite the inequality 2x + 3y < 6 in 'y=' form.

Back

y < -\frac{2}{3}x + 2.

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What is the solution set of the inequalities x + y > 3 and x - y < 1?

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The solution set is the region where both inequalities are satisfied, which can be found by graphing.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Shade the appropriate region for each inequality. 3. Identify the overlapping shaded region as the solution.

Front

What does it mean for a solution to be 'feasible' in the context of inequalities?

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A feasible solution is a point that satisfies all constraints (inequalities) in a system.