Systems of Equations: Application (1)

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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 to the system is the set of values that satisfy all equations simultaneously.

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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 does it mean to solve a system of equations graphically?

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To solve a system of equations graphically means to plot the equations on a graph and find the point(s) where they intersect, which represents the solution.

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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 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 how changes in one variable affect the other.

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How can you check if your solution to a system of equations is correct?

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Substitute the solution back into the original equations to see if it satisfies all equations in the system.

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What is a feasible region in the context of systems of equations?

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The feasible region is the area on a graph where all constraints of the system of equations are satisfied, typically represented by the intersection of the graphs.

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What is the role of constants in a system of equations?

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Constants represent fixed values in the equations that do not change, affecting the position and slope of the lines when graphed.

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How do you interpret the solution of a system of equations in a real-world context?

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The solution represents the values of the variables that satisfy all conditions of the problem, often corresponding to quantities or amounts in a real-world scenario.