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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?
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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 $x^2 + y^2 = 6$?
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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 $y = x^2 - 14$?
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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.
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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?
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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?
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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?
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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 $-x + y = -11$.
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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?
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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?
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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.
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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?
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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?
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