Math Test: Linear Inequalities and Systems, Area Model, Exponent Rules

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Questions and Answers

When graphing linear inequalities on a graph, the shaded area represents the solutions that satisfy the ______.

inequality

In solving linear inequalities, pay attention to the sign change when multiplying or dividing by a negative number to correctly ______ the inequality.

flip

The substitution method in linear systems involves replacing one variable with an expression to find the ______ solution.

unique

When graphing systems of linear inequalities, the overlapping shaded region indicates the ______ solutions of the system.

<p>feasible</p>
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Using the area model helps in visualizing the multiplication of numbers to find the total ______.

<p>area</p>
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When solving a system of linear inequalities, what does it mean if the shaded region on the graph is empty?

<p>There are no solutions to the system (D)</p>
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In linear inequalities, what is the key point to remember about switching the inequality sign when multiplying or dividing by a negative number?

<p>The inequality sign should be changed to the opposite direction (D)</p>
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When graphing a system of linear inequalities, what does it mean if the shaded regions overlap completely?

<p>The system has infinitely many solutions (B)</p>
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In linear systems, what is the main purpose of using the substitution method?

<p>To find the unique solution to the system (D)</p>
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When graphing linear inequalities on a number line, what does it signify when the open circle is on a specific value?

<p>That value is not included in the solutions (D)</p>
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Flashcards

Shaded area in linear inequalities

The shaded area represents all points that satisfy the inequality.

Sign change in inequalities

When multiplying or dividing by a negative number, you must reverse the direction of the inequality sign.

Substitution method

Replacing one variable to solve for a unique solution.

Overlapping shaded region

The overlapping region represents the set of points that satisfy all inequalities in the system.

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Area model in multiplication

Helps visualize multiplication to illustrate the total area as the product.

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Empty shaded region

It signifies that there are no values that satisfy all inequalities in the system simultaneously.

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Key point of sign change

Always remember to switch the inequality sign when you multiply or divide by a negative number.

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Overlapping regions completely

It means that any value within that whole region satisfies both inequalities.

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Purpose of using substitution method

To isolate one variable and then put it into another equation.

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Open circle on number line

That specific value is not a solution to the linear inequality.

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