Lesson 19 Formulating a System of Equations

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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 simultaneously.

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Define variables in a word problem.

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Variables are symbols used to represent unknown quantities in mathematical expressions or equations, often denoted by letters such as x, y, or z.

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What does it mean to formulate a system of equations from a word problem?

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Formulating a system of equations involves translating the relationships and conditions described in a word problem into mathematical equations using variables.

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How do you represent the total number of items sold in a word problem?

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You can represent the total number of items sold by creating an equation that sums the quantities of each type of item, often set equal to the total.

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What is the significance of defining relationships between variables in a system of equations?

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Defining relationships helps to create equations that express how the variables interact, which is essential for finding a solution to the system.

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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 down the equations based on the relationships described in the 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.

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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 does it mean for a system of equations to be consistent?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.