Quadratic Linear system

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What is a quadratic linear system?

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A system of equations that includes at least one quadratic equation and one linear equation.

Tags

CCSS.HSA.REI.C.7

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How many solutions can a quadratic linear system have?

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A quadratic linear system can have no solutions, one solution, or two solutions.

Tags

CCSS.HSA.REI.C.7

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What does it mean if a system has no solutions?

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It means that the graphs of the equations do not intersect.

Tags

CCSS.8.EE.C.8A

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What does it mean if a system has one solution?

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It means that the graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

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What does it mean if a system has two solutions?

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It means that the graphs of the equations intersect at two points.

Tags

CCSS.8.EE.C.8B

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What is the significance of the equal sign in inequalities?

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If an inequality has an equal sign (e.g., ≤ or ≥), it indicates that the boundary line is solid.

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CCSS.6.EE.B.8

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What is the significance of the inequality symbols > and

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These symbols indicate that the boundary line is dashed, meaning points on the line are not included in the solution.

Tags

CCSS.HSA.REI.D.12

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How do you determine the number of solutions in a linear-quadratic system?

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By analyzing the intersection points of the linear and quadratic graphs.

Tags

CCSS.HSA.REI.C.7

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What is the solution to the system: x - 3y = 8 and x + 3y = 2?

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(5, -1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the graphical representation of a quadratic equation?

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A parabola, which can open upwards or downwards.

Tags

CCSS.HSF-IF.C.7A