Writing Systems of Equations from Word Problems

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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 set of values that satisfy all equations in the system.

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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 the variable 't' represent in the context of fish prices?

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In the fish price problem, 't' represents the price of a tigerfish.

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What does the variable 'g' represent in the context of fish prices?

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In the fish price problem, 'g' represents the price of a goldfish.

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How do you write an equation for total cost in a word problem?

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What is the first step in solving a system of equations?

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The first step is to write the equations in a standard form, ensuring all variables are on one side and constants on the other.

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This equation represents the total cost 'y' of a pizza with 'x' toppings at Palanzio’s Pizzeria.

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This equation represents the total cost 'y' of a cheese pizza with 'x' toppings at Guido’s Pizza.

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How do you find the number of solutions in a system of equations?

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You can find the number of solutions by graphing the equations or using substitution or elimination methods.

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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 relationship between the variables in the equations.