Systems 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 a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the constraints given in the problem.

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CCSS.HSA.CED.A.3

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that make all equations in the system true.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What are the methods for solving systems of equations?

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The main methods are graphing, substitution, and elimination.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the substitution method?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the elimination method?

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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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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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What does it mean if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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CCSS.8.EE.C.8A

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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 by substituting the solution back into the original equations to see if they hold true.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is a linear equation?

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A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2