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Solve the system of equations. $\newline$ $y = x^2 + 44x + 4$ $\newline$ $y = 44x + 40$ $\newline$ 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 = x^2 + 44x + 4

\newline

y = 44x + 40

\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 $y$ . $x^2 + 44x + 4 = 44x + 40$
Subtract and Simplify: Subtract $44x + 4$ from both sides to set the equation to zero. $\newline$ $x^2 + 44x + 4 - 44x - 40 = 0$
Solve for $x^2$ : Simplify the equation. $\newline$ $x^2 - 36 = 0$
Find $x$ : Add $36$ to both sides to solve for $x^2$ . $\newline$ $x^2 = 36$
Calculate $y$ for $x=6$ : Take the square root of both sides to find $x$ . $x = \pm 6$
Calculate $y$ for $x=-6$ : Plug $x$ back into one of the original equations to find $y$ . Let's use $y = 44x + 40$ . $\newline$ First, for $x = 6$ : $y = 44(6) + 40$
Write Coordinates: Calculate $y$ for $x = 6$ . $\newline$ $y = 264 + 40$ $\newline$ $y = 304$
Write Coordinates: Calculate $y$ for $x = 6$ . $y = 264 + 40$ $y = 304$ Now, for $x = -6$ : $y = 44(-6) + 40$
Write Coordinates: Calculate $y$ for $x = 6$ .
$y = 264 + 40$
$y = 304$ Now, for $x = -6$ : $y = 44(-6) + 40$ Calculate $y$ for $x = -6$ .
$y = -264 + 40$
$y = -224$
Write Coordinates: Calculate $y$ for $x = 6$ . $\newline$ $y = 264 + 40$ $\newline$ $y = 304$ Now, for $x = -6$ : $y = 44(-6) + 40$ Calculate $y$ for $x = -6$ . $\newline$ $y = -264 + 40$ $\newline$ $y = -224$ Write the coordinates in exact form. $\newline$ First Coordinate: $x = 6$ $0$ $\newline$ Second Coordinate: $x = 6$ $1$

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