Non-Linear Systems

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What is a non-linear system?

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A non-linear system is a system of equations in which at least one equation is not linear, meaning it cannot be expressed in the form y = mx + b.

Tags

CCSS.HSA.REI.C.7

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What is the graphical method for solving non-linear systems?

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The graphical method involves plotting the equations on a graph and identifying the points where the curves intersect, which represent the solutions.

Tags

CCSS.HSA.REI.C.7

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What does it mean for a system to have multiple solutions?

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A system has multiple solutions when there are several points of intersection between the graphs of the equations, indicating more than one set of values that satisfy all equations.

Tags

CCSS.8.EE.C.8B

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What is the significance of the intersection points in a non-linear system?

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The intersection points represent the solutions to the system, where the values of the variables satisfy all equations simultaneously.

Tags

CCSS.HSA.REI.C.7

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How can you determine if a solution is valid in a non-linear system?

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To determine if a solution is valid, substitute the values back into the original equations to see if they hold true.

Tags

CCSS.HSA.REI.C.7

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What is a quadratic equation?

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A quadratic equation is a polynomial equation of degree 2, typically in the form ax^2 + bx + c = 0.

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How do you find the vertex of a parabola represented by a quadratic equation?

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The vertex of a parabola can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the quadratic function.

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What is the discriminant in a quadratic equation?

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The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac, which determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

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What does a positive discriminant indicate?

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A positive discriminant indicates that the quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

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What does a negative discriminant indicate?

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A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

Tags

CCSS.HSA-REI.B.4B