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

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How do you represent the perimeter of a rectangle in terms of its length and width?

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The perimeter P of a rectangle can be represented as P = 2l + 2w, where l is the length and w is the width.

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What does it mean when a word problem states that one quantity is 'less than' another?

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It indicates a subtraction relationship. For example, if the length is '4 meters less than' three times the width, it can be expressed as l = 3w - 4.

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How can you express the total number of coins in a word problem involving different types of coins?

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You can express the total number of coins by using a variable for each type of coin and setting up an equation that sums them. For example, if p is pennies and n is nickels, then p + n = total number of coins.

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What is the relationship between the number of animals and their legs in a barn problem?

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The relationship can be expressed using a system of equations where one equation represents the total number of animals and another represents the total number of legs. For example, x + y = total animals and 4x + 2y = total legs.

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How do you set up an equation for total revenue from ticket sales?

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You can set up an equation by multiplying the price of each type of ticket by the number of tickets sold and summing them. For example, if x is adult tickets and y is student tickets, the equation would be 4.50x + 2.50y = total revenue.

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What is the significance of defining variables in word problems?

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Defining variables helps to translate the problem into mathematical equations, making it easier to solve for unknown quantities.

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How do you determine the number of equations needed in a system?

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The number of equations needed typically corresponds to the number of variables you are trying to solve for. For example, to find two unknowns, you need at least two equations.

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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 system of equations based on the information provided in the word problem.

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

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You can check the solution by substituting the values back into the original equations to see if they hold true.