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Solve the system of equations. $\newline$ $y = 47x^2 + 8x - 20$ $\newline$ $y = 8x + 27$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Solve a system of linear and quadratic equations

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Q. Solve the system of equations.

\newline

y = 47x^2 + 8x - 20

\newline

y = 8x + 27

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $47x^2 + 8x - 20 = 8x + 27$
Subtract to Zero: Subtract $8x$ and $27$ from both sides to set the equation to zero. $\newline$ $47x^2 + 8x - 20 - 8x - 27 = 0$ $\newline$ $47x^2 - 47 = 0$
Isolate $x^2$ Term: Add $47$ to both sides to isolate the $x^2$ term. $\newline$ $47x^2 = 47$
Divide by $47$ : Divide both sides by $47$ to solve for $x^2$ . $\newline$ $x^2 = 1$
Take Square Root: Take the square root of both sides to solve for $x$ . $x = \pm 1$
Find $y$ for $x=1$ : Plug $x = 1$ into the second equation $y = 8x + 27$ to find the corresponding y-value. $\newline$ $y = 8(1) + 27$ $\newline$ $y = 35$
Find $y$ for $x=-1$ : Plug $x = -1$ into the second equation $y = 8x + 27$ to find the corresponding y-value. $\newline$ $y = 8(-1) + 27$ $\newline$ $y = 19$

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