Nonlinear Systems

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What is a nonlinear system?

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A nonlinear 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.

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CCSS.HSA.REI.C.7

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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 when the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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How do you identify the solution to a system of nonlinear equations graphically?

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The solution is the point(s) where the graphs of the equations intersect.

Tags

CCSS.HSA.REI.C.7

Front

What is the first step in solving the system: y = x^2 + 3x - 5 and y = x + 3?

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Set the equations equal to each other: x^2 + 3x - 5 = x + 3.

Tags

CCSS.HSA.REI.C.7

Front

What is the significance of the discriminant in a quadratic equation?

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The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, two real solutions; if zero, one real solution; if negative, no real solutions.

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CCSS.HSA-REI.B.4B

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

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

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CCSS.8.EE.C.8B

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What is the graphical representation of the equation y = x^2?

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The graph is a parabola that opens upwards with its vertex at the origin (0,0).

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CCSS.HSF-IF.C.7A

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How can you determine if a system of equations is independent?

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A system is independent if it has exactly one solution, meaning the lines intersect at a single point.

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CCSS.8.EE.C.8B

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What is the method of substitution in solving systems of equations?

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The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the method of elimination in solving systems of equations?

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The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6