Readiness - Systems

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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 is the point(s) where the equations intersect on a graph.

Tags

CCSS.8.EE.C.8B

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

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A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

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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 other variable.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you determine if a point is a solution to a system of equations?

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To determine if a point is a solution, substitute the x and y values of the point into each equation. If both equations are true, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the plot of the equations on a coordinate plane, where the intersection points represent the solutions.

Tags

CCSS.8.EE.C.8B

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What does it mean for a system of equations to be consistent?

Back

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

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solutions, meaning the lines are parallel and do not intersect.

Tags

CCSS.8.EE.C.8A

Front

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

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The coefficients determine the slope and position of the lines represented by the equations, affecting their intersection and the nature of the solutions.

Tags

CCSS.8.EE.C.8B

Front

How can you tell if two equations represent the same line?

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Two equations represent the same line if they are equivalent, meaning one can be transformed into the other through algebraic manipulation.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2