Unit 3 Test Review: Systems of Equations and Inequalities

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What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share 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 represent a budget constraint in a system of inequalities?

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A budget constraint can be represented as an inequality where the total cost of items does not exceed a certain amount. For example, if drinks cost $3 and hamburgers cost $5, the inequality would be: 3d + 5h ≤ 40.

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What does the solution to a system of equations represent graphically?

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The solution to a system of equations represents the point(s) where the graphs of the equations intersect.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

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

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How can you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, which never intersect.

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What is the first step in solving the system of equations 8x + 14y = 4 and 12x + 14y = 20 using elimination?

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The first step is to eliminate one of the variables by subtracting one equation from the other, leading to -4x = -16.

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What is the solution to the system of equations 3x + 2y = 12 and 3x = 6?

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The solution is (2, 3).

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What does the term 'dependent' mean in the context of systems of equations?

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Dependent equations are equations that represent the same line, resulting in infinitely many solutions.

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What does the term 'independent' mean in the context of systems of equations?

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Independent equations are equations that represent different lines, resulting in a unique solution.