Writing Systems of Equations and Inequalities

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other.

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How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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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 remaining variable.

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What is a feasible region in the context of inequalities?

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The feasible region is the set of all possible points that satisfy a system of inequalities, often represented graphically.

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What does it mean for a solution to be a 'bounded' solution in inequalities?

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A bounded solution means that the feasible region is enclosed, and there are limits to the values that the variables can take.

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What is the graphical method for solving systems of equations?

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The graphical method involves plotting each equation on a graph and identifying the point(s) where the lines intersect.

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

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Coefficients represent the relationship between the variables in the equations; they determine the slope and position of the lines when graphed.