5.3 PRACTICE - Writing Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

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How do you represent the cost of items in a system of equations?

Back

You can represent the cost of items by assigning variables to each item and creating equations based on the total cost.

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Write a system of equations for the following scenario: The cost of 5 squash and 2 zucchini is $1.32, and 3 squash and 1 zucchini cost $0.75.

Back

5q + 2z = 1.32 and 3q + 1z = 0.75.

Front

What does 'q' and 'z' represent in the equation 5q + 2z = 1.32?

Back

In this equation, 'q' represents the cost of one squash, and 'z' represents the cost of one zucchini.

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How do you determine the number of adults and children from ticket sales?

Back

You can set up a system of equations where one equation represents the total number of tickets sold and the other represents the total revenue from ticket sales.

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Write a system of equations for the following scenario: 3247 people attended a fair, with adults paying $5 and children $3, collecting a total of $14,273.

Back

5a + 3c = 14,273 and a + c = 3247.

Front

What do 'a' and 'c' represent in the equation 5a + 3c = 14,273?

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In this equation, 'a' represents the number of adults, and 'c' represents the number of children.

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How can you solve a system of linear equations?

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You can solve a system of linear equations using methods such as substitution, elimination, or graphing.

Front

Write a system of equations for the following scenario: A theater sold 200 tickets for $1304, with adults paying $8 and children $4.

Back

a + c = 200 and 8a + 4c = 1304.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.