Unit 2-3 Review: Writing Systems of Equations & Inequalities

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What is a system of inequalities?

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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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Back

This inequality represents a minimum requirement, indicating that the total amount of two items (x and y) must be at least 50 units.

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How do you set up a system of equations from word problems?

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Identify the variables, translate the relationships and conditions into equations, and ensure that the equations represent the problem accurately.

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What is the significance of the coefficients in a system of equations?

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Coefficients represent the rate of change or the contribution of each variable to the total. They are crucial for understanding the relationship between the variables.

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How do you interpret the solution of a system of equations graphically?

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The solution of a system of equations is represented by the point(s) where the graphs of the equations intersect. This point(s) satisfies all equations in the system.

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

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A system of equations has no solution if the lines represented by the equations are parallel, meaning they never intersect.

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

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A system of equations 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 point is a solution to a system of equations?

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Substitute the coordinates of the point into each equation in the system. If the point satisfies all equations, it is a solution.

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What is the difference between a linear equation and a linear inequality?

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A linear equation represents a straight line and has an equal sign, while a linear inequality represents a region of the graph and uses inequality signs (>, <, ≥, ≤).