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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for a system of equations to have a unique solution?

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A system of equations has a unique solution if there is exactly one set of values for the variables that satisfies all equations in the system.

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CCSS.8.EE.C.8B

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution if there are no values for the variables that can satisfy all equations simultaneously, often due to parallel lines.

Tags

CCSS.8.EE.C.8B

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What does it mean for a system of equations to have infinitely many solutions?

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A system of equations has infinitely many solutions if there are an infinite number of values for the variables that satisfy all equations, typically when the equations represent the same line.

Tags

CCSS.8.EE.C.8B

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How can you determine if two lines represented by equations are parallel?

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Two lines are parallel if they have the same slope but different y-intercepts.

Tags

CCSS.8.EE.B.5

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What is the substitution method for 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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the elimination method for 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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the graphical method for solving systems of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

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What is the significance of the point of intersection in a system of equations?

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The point of intersection represents the solution to the system, indicating the values of the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8B

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How do you check if a solution is correct for a system of equations?

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To check if a solution is correct, substitute the values of the variables back into the original equations to see if they hold true.