5.3 WORK - Writing Systems of Equations

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What is a system of equations?

Back

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 the total number of coins in a word problem?

Back

You can represent the total number of coins using a variable equation, such as p + n = total, where p is the number of pennies and n is the number of nickels.

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What does the equation 0.01p + 0.05n = 1.03 represent?

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This equation represents the total value of pennies (p) and nickels (n) in dollars, where 0.01 is the value of a penny and 0.05 is the value of a nickel.

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

Back

Identify the variables, write equations based on the relationships described in the problem, and ensure the equations represent the same situation.

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

Back

Coefficients represent the rate or quantity of each variable in the equations, indicating how much each variable contributes to the total.

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What does the equation S + A = 530 represent in a ticket sales problem?

Back

This equation represents the total number of student tickets (S) and adult tickets (A) sold, which adds up to 530.

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

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The solution of a system of equations represents the values of the variables that make all equations true simultaneously.

Front

What is the purpose of using variables in equations?

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Variables are used to represent unknown quantities in equations, allowing us to solve for these quantities based on given information.

Front

What does the equation 3S + 4A = 1740 represent?

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This equation represents the total revenue generated from selling student tickets (S) at $3 each and adult tickets (A) at $4 each, totaling $1740.

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How can you verify the solution of a system of equations?

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