3A - Formulating a System 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 to the system is the set of values that satisfy all equations simultaneously.

Front

How do you represent the sum of three numbers in an equation?

Back

Front

What does it mean for one number to be the product of two others?

Back

Front

How can you express the quotient of two numbers in an equation?

Back

Front

What is the relationship between variables in a system of equations?

Back

The relationship can be linear, quadratic, or involve other mathematical operations, and it defines how the variables interact with each other.

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and ensure all equations represent the same scenario.

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

Back

Coefficients represent the numerical factors that multiply the variables, indicating the weight or influence of each variable in the equation.

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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.

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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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.