Step 1 :

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a.

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The linear quadratic system is \"\" and \"\".

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Substitute \"\" in \"\".

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\"\"

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Step 2 :

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Solve the equation \"\".

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By factoring by grouping.

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\"\"

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If \"\", then \"\".

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If \"\", then \"\".

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The intersection points are \"\" and \"\".

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Check :

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Substitute the point \"\" in

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\"\"

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Since the above statement is true, \"\" is a intersection point of The linear quadratic system is \"\" and \"\".

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Substitute the pioint \"\"

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\"\"

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Since the above statement is true, \"\" is a intersection point of the linear quadratic system is \"\" and \"\".

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Solution :

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The intersection points are \"\" and \"\".

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Step 1 :

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b.

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The linear quadratic system is \"\" and \"\".

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Substitute \"\" in \"\".

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\"\"

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Step 2 :

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Solve the equation \"\".

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By factoring by grouping.

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\"\"

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\"\"

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If \"\", then \"\".

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If \"\", then

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\"\".

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The intersection points are \"\" and \"\".

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Check :

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To check the solution, substitute the point \"\" in \"\".

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\"\"

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Since the above statement is true, \"\" is a intersection point of the linear quadratic system \"\" and \"\".

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To check the solution, substitute the point \"\" in \"\".

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\"\"

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Since the above statement is true, \"\" is a intersection point of the linear quadratic system \"\" and \"\".

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Solution :

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The intersection points are \"\" and \"\".

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Step 1 :

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c.

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The linear quadratic system is \"\" and \"\".

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Substitute \"\" in \"\".

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\"\"

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Step 2 :

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Solve the equation \"\".

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\"\" is a quadratic equation, use quadratic formula to find the solution of the related quadratic equation.

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Solution \"\".

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Compare the equation with standard form of the quadratic equation \"\".

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\"\".

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Solution

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\"\"

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\"\".

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If \"\", then

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\"\".

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If \"\", then

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\"\"

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The intersection points are imaginary points.

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They are \"\" and \"\".

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Check :

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To check the solution, substitute the point \"\" in \"\".

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\"\"

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Since the above statement is true, \"\" is a intersection point of the linear quadratic system  \"\" and \"\".

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To check the solution, substitute the point \"\" in \"\".

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\"\"

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Since the above statement is true, \"\" is a intersection point of the linear quadratic system \"\" and \"\".

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Solution :

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The imaginary intersection points are \"\" and \"\".