Podcast
Questions and Answers
What is the method used to solve the system of nonlinear equations for the first exercise?
What is the method used to solve the system of nonlinear equations for the first exercise?
Graphing.
When using substitution to solve the equation $y = x^2 - 3$, what expression do you substitute for y in the second equation?
When using substitution to solve the equation $y = x^2 - 3$, what expression do you substitute for y in the second equation?
$x^2 - 3$.
How do you apply the elimination method in the system $3x - y = 5$ and $x^2 - 3x - y = -6$?
How do you apply the elimination method in the system $3x - y = 5$ and $x^2 - 3x - y = -6$?
Combine the equations to eliminate y and solve for x.
In the equation of the circle $x^2 + y^2 = 6$, what geometric shape does it represent?
In the equation of the circle $x^2 + y^2 = 6$, what geometric shape does it represent?
What is the graphical relationship between the constant function $y = 2$ and the circle described by $x^2 + y^2 = 6$?
What is the graphical relationship between the constant function $y = 2$ and the circle described by $x^2 + y^2 = 6$?
What is the solution to the system of equations given by $y = - 2x + 1$ and $y = x^2 - 14$?
What is the solution to the system of equations given by $y = - 2x + 1$ and $y = x^2 - 14$?
Describe the relationship if a nonlinear system contains a constant function and a quadratic function with one solution.
Describe the relationship if a nonlinear system contains a constant function and a quadratic function with one solution.
In the system $12x^2 - y = 64x - 76$, if you rewrite it for elimination, what can you express y as?
In the system $12x^2 - y = 64x - 76$, if you rewrite it for elimination, what can you express y as?
How would you approach solving the system of equations given by $y = x + 6$ and $y = (x + 2) - 3$ by graphing?
How would you approach solving the system of equations given by $y = x + 6$ and $y = (x + 2) - 3$ by graphing?
For the system consisting of $y = x^2 - 4x$ and $y = x - 4$, what method would you use to solve it?
For the system consisting of $y = x^2 - 4x$ and $y = x - 4$, what method would you use to solve it?
Explain how elimination can be used to solve the system $x^2 - 5x - y = 2$ and $-x + y = -11$.
Explain how elimination can be used to solve the system $x^2 - 5x - y = 2$ and $-x + y = -11$.
When graphing the equations $y = 3x^2 - 4x + 3$ and $y = 2x - 3$, what are you looking for?
When graphing the equations $y = 3x^2 - 4x + 3$ and $y = 2x - 3$, what are you looking for?
What characteristic do the graphs of a constant function and a circle exhibit if they have two solutions?
What characteristic do the graphs of a constant function and a circle exhibit if they have two solutions?
Describe how you would solve the system $x^2 + y^2 = 25$ and $y = 5 - x$ using substitution.
Describe how you would solve the system $x^2 + y^2 = 25$ and $y = 5 - x$ using substitution.
What general steps would you follow to solve a nonlinear system using graphing?
What general steps would you follow to solve a nonlinear system using graphing?
How does the method of graphing differ when solving systems of linear equations versus nonlinear equations?
How does the method of graphing differ when solving systems of linear equations versus nonlinear equations?
Flashcards
Nonlinear System
Nonlinear System
A system of equations where at least one equation is non-linear, meaning it doesn't form a straight line when graphed. Examples include quadratic equations and circles.
Solving by Graphing
Solving by Graphing
A method to solve a system of equations by plotting the graphs of each equation and finding the points of intersection. These points represent the solutions to the system.
Solving by Substitution
Solving by Substitution
A method to solve a system of equations by substituting the expression for one variable from one equation into the other equation. This allows you to solve for one variable, then substitute it back to find the other.
Solving by Elimination
Solving by Elimination
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Nonlinear System of Equations
Nonlinear System of Equations
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Substitution Method
Substitution Method
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Elimination Method
Elimination Method
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Solution of a Nonlinear System
Solution of a Nonlinear System
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Inconsistent Nonlinear System
Inconsistent Nonlinear System
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Dependent Nonlinear System
Dependent Nonlinear System
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Solving a Nonlinear System
Solving a Nonlinear System
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Solving a Nonlinear System by Graphing
Solving a Nonlinear System by Graphing
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