8.EE.8 Systems of Equations

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean to solve a system of equations by elimination?

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It means to eliminate one variable by adding or subtracting the equations, 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 the graphical interpretation of a system of equations?

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The solutions of a system of equations can be represented as the points where the graphs of the equations intersect.

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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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It means that 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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It means that the equations represent the same line, so every point on the line is a solution.

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CCSS.8.EE.C.8A

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How can you determine if a system of equations has one solution?

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If the lines represented by the equations intersect at exactly one point, the system has one solution.

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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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It involves solving one equation for one variable and 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 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.

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CCSS.8.EE.C.8A

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How do you identify a consistent system of equations?

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A consistent system 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 has no solutions, meaning the lines are parallel.

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CCSS.8.EE.C.8A