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Solve the system of equations. $\newline$ $y = 44x + 50$ $\newline$ $y = x^2 + 44x - 50$ $\newline$ 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: parabolas

Full solution

Q. Solve the system of equations.

\newline

y = 44x + 50

\newline

y = x^2 + 44x - 50

\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 $y$ . $44x + 50 = x^2 + 44x - 50$
Subtract $x$ Term: Subtract $44x$ from both sides to get rid of the $x$ term on one side. $\newline$ $50 = x^2 - 50$
Add to Isolate $x^2$ : Add $50$ to both sides to isolate the $x^2$ term. $\newline$ $100 = x^2$
Take Square Root: Take the square root of both sides to solve for $x$ . $x = \pm 10$
Plug $x = 10$ : Plug $x = 10$ into one of the original equations to find the corresponding $y$ value. $\newline$ $y = 44(10) + 50$ $\newline$ $y = 440 + 50$ $\newline$ $y = 490$
Plug $x = -10$ : Plug $x = -10$ into the same equation to find the other $y$ value. $\newline$ $y = 44(-10) + 50$ $\newline$ $y = -440 + 50$ $\newline$ $y = -390$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(10, 490)$ $\newline$ Second Coordinate: $(-10, -390)$

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