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

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

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CCSS.HSA.CED.A.3

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

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CCSS.6.EE.A.1

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

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CCSS.6.EE.C.9

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

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

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CCSS.HSA.REI.C.7

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

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

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CCSS.8.EE.C.8C

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

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

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CCSS.8.EE.C.8B

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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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CCSS.8.EE.C.8B

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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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CCSS.8.EE.C.8A

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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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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6