Writing Systems of Linear Equations

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What is a linear equation?

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A linear equation is an equation that represents a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does it mean to solve a system of linear equations?

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To solve a system of linear equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the graphical representation of a system of linear equations?

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The graphical representation of a system of linear equations consists of the lines corresponding to each equation. The point(s) where the lines intersect represent the solution(s) of the system.

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CCSS.8.EE.C.8B

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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

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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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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is a consistent system of equations?

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

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CCSS.8.EE.C.8A

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solutions, meaning the lines are parallel and never intersect.

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CCSS.8.EE.C.8A

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

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CCSS.8.EE.C.8B

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How do you write a system of equations from a word problem?

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To write a system of equations from a word problem, identify the variables, translate the relationships and conditions into equations, and ensure they represent the situation accurately.

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CCSS.HSA.CED.A.3

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What is the importance of the coefficients in a linear equation?

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The coefficients in a linear equation determine the slope and the direction of the line when graphed.